LEVEL 01 \\ Starter Level 1.1 Ground-to-Ground Projectile 1 Aparticle is projected with speed 10 m/s at an angle 60° with horizontal. Find (a) time of flight, (b) range, (c) maximum height, (d) speed of particle after one second (e) and velocity when height of the particle is 1 m. , 2 Abody is projected with a speed of 30 ms~* at an angle of 30° with the vertical. Find the maximum height, time of flight and the horizontal range of the motion. [Take, g=10m/s?] 3 3 The velocity of projection of a projectile is given by u = Sit 10}. Find (a) time of flight, (b) maximum height (c) and range. 4 Aparticle is projected with velocity 20 m/s at an angle of 45° with horizontal. Find out 7 (a) for which angle is T maximum, Tmax =? (b) for which angle is R maximum, Rinax =? 5 Two bodies are projected at angles 6 and (90° — 6) to the horizontal with the same speed. Find the ratio of their (a) times of flight, (b) maximum heights _(c) and horizontal ranges. 6 Abody is so projected in the air that the horizontal range covered by the body is equal to the vertical height attained by the body. Find the angle of projection. | A projectile can have the same range R for two angles of projections. (a) Hash andT, be the times of flight in two cases, then find out relation between T,,T2 and R. ? (b) If, andH, are maximum heights in two cases, find the sum of the maximum heights. (c) Find product of H, andH,, N @ scanned with OKEN Scanner8 Acticketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball? .° - anne 1 The equation of a projectile is y = /3x "2 8x”, find the angle of projection and also find the speed of projection. 10 Aball is thrown upward at an angle of 45° with the horizontal and lands on the top edge of a building that is 20 m away. The top edge is 12 m above the throwing point. Find the initial speed of the ball in m/s. (Take, g = 10 m/s?) 11 Find the value of @ in the diagram given below, so that the projectile can hit the target. v=20 m/s n=10m x=20m 12 Aprojectile is thrown with a speed of 100 m/s making an angle of 60° with the horizontal. Find the time after which its inclination with the horizontal is 45°. 13. Astoneis thrown with a velocity u at an angle o: with horizontal. Find its speed when it makes an angle B with the horizontal. 14 Aparticle is thrown with initial speed u at an angle 0 w.r.t. horizontal. Find the time after which velocity of the projectile becomes perpendicular to the initial velocity. 15 Alarge number of bullets are fired in all directions with the same speed v. What is the maximum area on the ground on which these bullets will spread? 16 Aparticle is projected at an angle of 30° w.r.t: horizontal speed 20 m/s. Find (2) the position vector of the particle after 1 s. (b) the angle between velocity vector and position vector att = 1s. 17 Aplayer kicks a football at an angle of 45° with an initial speed of 20 m/s. A second player on the goal line 60 m away in the direction of kick starts running to receive the ball at that instant. Find the speed of the second player with which he should run to catch the ball before it hits the ground. [Take, g =10 m/s?] 18 Amanis sitting on the shore of a river. He is in the line of a 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that, the point of projection and the edge of the boat are in the same horizontal level. 1 8 A ball is thrown from ground level so as to just clear a wall 4 m high at a distance of 4m and falls at a distance of 14 m from the wall. Find the magnitude and direction of initial velocity of the ball. 1.2 Projection from Certain Height 1 Aprojectile is fired horizontally with a speed of 98 ms~? from the top of a hill 490 m high. Find {a) the time taken to reach the ground, (b) the distance of the target from the hill (c) and the velocity with which the projectile hits the ground, (Take, g =9.8 m/s?) @ scanned with OKEN ScannerN a a on ‘Two stones A and B are projected simultaneously from the top of a 100 m high tower. Stone g is projected horizontally with speed 10 m/s and stone A is dropped from the tower. Find out the following (Take, g = 10 m/s”) {a) time of flight of the two stones, (b) distance between two stones after 3's, (C) angle of strike of B with ground (d) and horizontal range of particle B. ‘Two paper screens A and B are separated by a distance of 100 m. A bullet pierced A and then g The hole in Bis 10 cm below the hole in A. If the bullet is travelling horizontally at the time of | hitting the screen A, calculate the velocity of the bullet when it hits the screen A. Neglect the resistance of paper and air. ‘motorcycle stunt rider rides off the edge of a cliff. Just at the edge his velocity is horizontal with magnitude 9.0 m/s. Find the motorcycle’s position, distance from the edge of the cliff and velocity after 0.5 s. ‘An object is thrown between two tall buildings 180 m from each other. The object is thrown horizontally from a window 55 m above ground from one building through a window 10.9 m above ground in the other building. Find out the speed of projection. (Use, g =9.8 m/s”) From the top of a 11 m high tower, a stone is projected with speed 10 m/s at an angle of 37° as shown in figure. Find Y (a) time of flight, (b) horizontal range (C) and speed just before striking the ground. From the top ofa 11 m high tower, a stone is projected with speed 10 m/s at an angle of 37° as shown in figure. Find Y (2) speed after 2 s, (b) time of flight, (0) horizontal range, (d) the maximum height attained by the particle (e) and speed just before striking the ground, @ scanned with OKEN Scanner8 An object is thrown horizontally from a point A from a tower and hits the ground 3 s later at B. The line from A to B makes an angle of 30° with the horizontal. Find the initial velocity of the object. (Take, g = 10 m/s?) ane v 9 Abody is projected horizontally from the top of a tower with initial velocity 18 ms~*. It hits the ground at angle 45°. What is the vertical component of velocity when it strikes the ground? 10 ABomber flying upward at an angle of 53° with the vertical releases a bomb at an altitude of 800 m. The bomb strikes the ground 20 s after its release. Find (a) the velocity of the bomber at the time of release of the bomb, {b) the maximum height attained by the bomb, {c) the horizontal distance travelled by the bomb before it strikes the ground (d) and the velocity (magnitude and direction) of the bomb just when it strikes the ground. [Given, sin 53° = 08, 3 = 10ms~?] 1.3 Projection on Inclined Plane 1 Abullet is fired from the bottom of the incline plane with speed 50 m/s at an angle @ =37° with: the inclined plane. The angle of incline is 30° with the horizontal. Find (a) the position of the maximum height of the bullet from inclined plane, (b) time of flight, (c) horizontal range along the incline, (d) for what value of @ will range be maximum (e) and maximum range. 2. Aparticle is projected horizontally with speed u from the top of a plane inclined at an angle with horizontal. How far from the point of projection will the particle strike the plane? 3. Aprojectile is thrown at an angle @ with an inclined plane of inclination fas shown in figiir= Find the relation between B and, if (2) projectile strikes the inclined plane perpendicularly (b) and projectile strikes the inclined plane horizontally. 4 Aparticle is projected at an angle @ with an inclined plane making an angle B with the horizontal as shown in figure. Initial speed of the particle is u. After time t, find Xaxis Yaxis u B (a) x-component of acceleration, (b) y-component of acceleration, (c) x-component of velocity, (d) y-component of velocity, {e) x-component of displacement, (f) y-component of displacement {g) and y-component of velocity when particle is at maximum distance from the incline plane. @ scanned with OKEN ScannerLevel 1 1.1 Ground-to-Ground Projectile 4. (a) 35 (b) v3 m 2 m(d) 10 1 3V3 5, 453 m aT mis (eyv=si + V5) o. = 45°,40m 3. (a) 2s (b) 5m (c) 10m 4, (a)0=90°, 4 5 (b)O= 4 nent at 7 7. (a) TyTg=— (b) & (ej? 5,(a) tan@: 1 (b) tan? @:1.(c) 1:4 6. @=tan*(4) me OF 8, 50m 9. @=60°,2m/s 10. 10/5 m/s 11. 0= 45°, tan“* (3) 12, t=5(v3-1)s 43. ucosasecB 14, t= tense 15, Maximum area = [a 46, (a)r=10V81 +5), Ini=yaova)? +5? (by@= cos ‘(2 Fe 17. 5¥2 m/s (9? 18. Oe [15°, 18.5°] U[71.5°, 75°] 19. o=tan a (3) 1.2 Projection from Certain Height 1. (a) 10s (b) 980 m (c) 98/2 ms“ at an angle of 45° 2. (2) V20's (b) 30 m (c) tan“ 24/5 (d) 20V5 m 3. 700 m/s . 4, x=4. smy=3 m r= Bn The component of velocity at this time are v,. =9.0m/s and vy =5 m/s. 6. (a) 4.5 (b) 8m (c) 8V5 m/s m (d) 12.8 m (e) 8V5 m/s —-5. u=60m/s 88 7. (a)Bi-14j (b) T= 2 5 (0) Range = 8, 15/3 m/s 9. 18 m/s 40. (a) 100 m/s (b) 980 m (c) 1600 (6) 0= ten (2) v= 2065 m/s 13 Projection on Inclined Plane 1. (a)30V3 m(b) 4V3s (©) 4olaf8 ~3) m (8) 20° (e) 2° m 2u? sin@ > 2 Re ose 3. (a)2 tan =cot B (b) 2 sin@= sin(0+B) cosB. 4. (a)—g sinB (b)-3 cos, (c) ucos6—g sinB xt (d) usind— 3cOsBxt(e]ucosOxt—5 3 sinB xt? (usin xt gcosBxt? (g) zero @ scanned with OKEN ScannerLEVEL 02\JEE Main Level ; ' ions ; Ne eae ed 5 jimes its maximum height. Its angle of projection 1 The horizontal range of a projectile is 4/3 times its will be (d) 30° ae ad ca n the fee plane is twice the P ‘i it or " 2 Aparticle is projected with a velocity v such that its ange 3 (where gis acceleration due to greatest height attained by it. The range of the proj gravity) 2 (a2 wm oe ol * : inetic ent 3 Acricket ball is hit at 30° with the horizontal with kinetic energy K. The kinetic energy at the highest point is 3K/4 (a) zero (Ka (on suche ir 4. Abody is thrown horizontally from the top of a tower of height 5 mi It ee the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is (take, g=10 ms) 2 a (a)25ms™ (b) Sms (c)10ms* (d) 20 ms’ 5. An aeroplane moving horizontally with a speed of 720 km/h drops a food pocket, while flying at a height of 396.9 m. The time taken by a food pocket to reach the ground and its horizontal range is (take, g =9.8 ms~*) (a) 3s and 2000 m (b) 5s and 500 m (c) 8s and 1500 m (d) 9s and 1800 m 6 Aball is rolled off the edge of horizontal table at a speed of 4 m/s. It hits the ground after 0.4 s, Which is statement given below is true ? (@) It hits the ground at a horizontal distance 2.6m from the edge of the table. (b) The speed with which it hits the ground is 4.0 m/s. . (c) Height of the table is 0.8 m. (d) It hits the ground at an angle of 60° to the horizontal. 7 The range of a particle when launched at an angle of 15° with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of 45° to the horizontal? (a) 1.5 km (b) 3.0 km (c) 6.0 km (d) 0.75 km 8 Acricketer hits a ball with a velocity of 25 m/s at 60° above the horizontal, How far above the Sround it passes over a fielder 50 m from the bat? (Assume the ball is struck very close to the ground) (2)8.2m (b) 9.0m (c) 11.6 m (d) 12.7 9 A stone is projected from the ground with velocity 25 m/s. 2s later, itJust clear & wall 5 m high. The angle of projection of the stone is (Take, g = 10 m/s?) aH GH 1 (a) 30° (b) 45° (c) 50,2° (d) 60° 1 0 Galileo writes that for angles of Projection of a projectile at angles (45° +6) and (45° —6), the horizontal ranges described by the projectile are in the ratio of (0 < 45°) (a)2:4 (b) 4:2 (cara (2:3 The greatest height t i The rests height to which aman can throw a stone ish, The greatest distance to which he h @> (yh (ah a (d) 3h @ scanned with OKEN Scanner12 1 3 15 16 Li 8 18 20 21 22 23 2 8 Abody of mass 0.5 kg is projected under gravity with a speed of 98 m/s at an angle of 30° with the heron The magnitude of change in momentum of the body by the time it hits the ground is (a) 24.5 N-s (b) 49.0 N-s (c) 98.0N-s (d) 50.0 N-s An object is projected with a velocity of 20 m/s making an’angle of 45° with horizontal. The equation for the trajectory is h = Ax — Bx?, where his height, x is horizontal distance and A & B are constants. The ratio A : Bis (take, g = 10 ms~*) (a)a5 (b)5:4. (c)4:40 (d) 40:4 A body of mass m is thrown upwards at an angle @ with the horizontal with velocity u. While rising up, the speed of the mass after t seconds will be (a) lu cos 6)? + (u sin @)? (b) J(u cos 0 gt)? + (using)? lu? + gt? — Qu sind) gt (a) Ju? + gt? — au cos 6) gt A cricketer can thrown a ball toa maximum horizontal distance of 100 m. The speed with which he throws the ball is (to the nearest integer) (a) 25ms* (b) 42 ms* (c) 31ms“ (d) 35 ms? Astone is thrown at an angle @ to the horizontal reaches a maximum height H, then the time of flight of stone will be @ & (o) af (2, [sine (@) 8 & 3 8 Aball is projected upwards from the top of tower with a velocity 50 ms“? making an angle 30° with the horizontal. The height of tower is 70 m. After how many second from the instant of throwing will the ball reach the ground? (a)2s (0) 5s 755. ys A body is projected horizontal from a height with speed 20 m/s. What will be its speed after 5s? (Take, g =10 m/s?) 7 (a) 54 m/s (b) 20 m/s (c) 50 m/s (d) 70 m/s. Astone is projected from the ground with velocity 50 m/s at an angle of 30°. It crosses a wall after 3.s. How far beyond the wall the stone will strike the ground? (Take, g = 10 m/s”) {a) 90.2m (b) 89.6 m (c)86.6m (d) 70.2 m A projectile is fired from level ground at an angle 8 above the horizontal. The elevation angled of the highest point as seen from the launch point is related to @ by the relation (a) tang=4 tan (b) tan 9 = tan@ (o)tan = tang (d) tang=2tand A boy aims at a bird from a point at a horizontal distance of 100 m.. The gun can impart a velocity of 500 ms~ to the bullet. At what height above the bird must he aim his gun in order to hit? (Take, g =10 ms) (a) 20cm (b) 40cm (c) 50cm (d) 100 cm Aparticle is projected at an angle of 45° from 8 m before the foot of a wall, just touches the top of the wall and falls on the ground of the opposite side at a distance 4 m from it. The height of wall is 2 4 8 3 (a) 3” (b) 3m ©) 3” (a) an A projectile is thrown with an initial velocity of v = al +bj. If the range of projectile is double of maximum height reached by it, then (a)a=2 (b)b=a (b=2a (a)b=4a The ceiling of a hall is 40 m high. For maximum horizontal distance, ‘the angle at which the ball can be thrown with a speed of 56 ms~? without hitting the ceiling of the hall is (a) 25° (b) 30° () 45° (d) 60° @ scanned with OKEN Scanner25 26 27 28 29 3, 32 33 From the top of a tower 19.6 m high, a ball is thrown horizontally. Ifthe line joining the point Projection to the point where it hits the ground makes an angle of 45° with the horizontal, then the initial velocity of the ball is (2) 9.8 ms (b) 4.9 ms“ (©) 14.7 ms (d) 2.8 ms ‘At what angle with the horizontal should a ball be thrown, so that its range R is related to the time of flight as R = 5T?? (Take, g = 10 ms~) (a) 30° (b) 45° (©) 60° {d) 90° One second after projection, a stone moves at an angle 45° with horizontal, 2s after proj it moves horizontally its angle of projection is [take, g = 10 m/s] (a) tan (V3) (b) tan“ (4) (c) tan“? (3) (d) tan (2) A particle is projected from ground with velocity u at an angle 6 to horizontal. Avera of particle between point of projection and maximum height of projectile is ae 1 +2c0s?@ (WS Vi c0s?@ (5 f1+3 cos? 6 (d)ucos 6 A particle is projected with a velocity u making an angle 6 with the horizontal. At any instant, itg velocity vis at right angles to its initial velocity u, then v is (a)ucos@ (b)utan@ (c)ucot® (d)u sec A projectile is aimed at a mark on a horizontal plane through the point of projection and falls 3m short when its elevation is 15° but overshoots the mark by 12 m when its elevation is 45°, The angle of elevation to hit the target on the horizontal plane is (a) 18.5° (b) 26.5° (c) 30° (4) 37° Horizontal range and maximum height of a projectile are R and H. Ifa constant horizontal acceleration a =4 given to projectile due to air, then what will be the horizontal range and maximum height of projectile? : wm sta8 to(e+#) an (OR +2H0,H (@R+H,H lection, 8 Velocity Velocity of a stone projected, 2 s before it reaches the maximum height, makes angle 53° with the horizontal, then the velocity at highest point will be - (a) 20 m/s (b) 15 m/s (c) 22 m/s (a) 2 m/s Aball is thrown up with a certain velocity at an angle @ to. the horizontal. The kinetic energy (KE) of the ball varies with height has _ . 1 1 Gu KE o b> oO qo 1 (Ke (Ke ° i ° ho @ scanned with OKEN Scanner‘ball is thrown up with a certain velocity at an angle @ to the horizontal. The kinetic energy (KE) of the ball varies with horizontal displacement x as I 1 @ Ke KE oS ° =, t t ane ee ° x ° > 35 Aprojectile is thrown with velocity 10/2 m/s at an angle 45° to horizontal. Calculate time interval between the moments when velocity is 125 m/s. (Take, g = 10 m/s?) (a)1.0s (15s (20s (a 05s 36 Aparticle is projected from point A with velocity us/2 at angle 45° to horizontal as shown in diagram. It strikes the plane BC at right angle. What is the velocity of particle at the time of impact? vu u Qu = 4 (d) {a) = (b) 3 () z (du 37 In above question, calculate time after which particle strikes the plane. i+) u t Bu B)u = (b) — (o— . (d) = o(& 3 Oe ag B-i)s + 38 Aball rolls off the top of a stairway with a horizontal velocity u m/s. If the steps are h metres high and w metres wide, then the ball will just hit the edge of the nth step is 2 2 2 (a) n= 2 (n= 24 (n= (n= gw? sw gtwe gu 39 An object is projected so that it just clears two vertical walls each of height 7.5 m and Separation 50 m. If time of passing between the two walls is 2.5 s, then find horizontal range of the object. (a) 70m (b) 75 m (c) 105m (a) 150m 40 Aballis projected from the top of a tower with a velocity 31 + 4] +5 ms™, where i, Jandie are unit vectors along east, north and vertical upwards, respectively. If the height of the tower is 30 m, its range is (g = 10 ms?) (b) 12m (b) 9m (c) 15m (a) 25m 41 Distance between a frog and an insect on a horizontal plane is 10 m. Frog can jump with a maximum speed of V0 m/s. Minimum number of jumps require by the frog to catch the insect is (take, g = 10 m/s?) (a) (b) 10 {c) 100 (a) So @ scanned with OKEN Scanner42 43 45 46 47 4 S 50 = 8 Aparticle is projected at an angle of elevation a and after t seconds it appears to have an ange of elevation Bas seen from the point of projection. The initial velocity will be 2g sin (a -B) sin (a -B) gtcosB (a) st Be cos Oe (OF Sina —B) 2sin (=) A stone is just released from the window of a train moving along a horizontal straight track, The stone will hit the ground following a {a) straight line path (b) circular path (©) parabolic path (d) hyperbolic path The trajectory of a projectile fired horizontally with velocity u is parabola given by =3_y? é exe ty=5>x oy xe% A fixed rifle is aimed at a point on a vertical wall 1440 m horizontally away and 1080 m high above the point of the rifle end. A bullet is fired at 150 m/s towards the target. 10 s after the firing, the gravitational field vanishes. At what height from ground the bullet will hit the vertica| wall? (g =10 m/s?) (a) 400m. (b) 420 m (c) 380 m (d) 250 m Aball is thrown at an angle @ with the horizontal. Its initial kinetic energy is 100 J and it becomes 75 J at half the maximum height. The angle of projection is (a ase (b) 30° (cos (3) (@) tant (8) A particle is fired with velocity u making angle 6 with the horizontal. What is the change in velocity when it is at the highest point? (a)-ucos® (bu ()-usino (4) (u cos @—u) A particle is projected upwards from the top of a tower with an initial velocity 40 m/s and ang) of projection 30° with the horizontal falls at a distance of 2001/3 from foot of tower. The heigh of tower is (take, g = 10 m/s”) (a) 160m (b) 200 m (c) 300 m. (d) None of these From the top of a tower of height h, a body of mass m is projected in the horizontal direction with a velocity v. It falls on the ground at a distance x from the tower. If a body of mass 2 mis projected from the top of another tower of height 2h in the horizontal direction so that it fall on the ground at a distance 2x from the tower, the horizontal velocity of the second body is (a)av (b) /2v wt ae 2 2 Ashot is fired with a velocity u at a very high vertical wall whose distance from the point of projection is x. The greatest height above the level of the point of project at which the bullet can hit the wall is u 4 4 g2x2 4g 2x2 4 gy? 492? (ay 8%x wyt=atx tzaix (gis? 2gu gu’ 4gu’ 2gu2 Three projectiles A, B and C are thrown from the same point in the same plane. Their” trajectories are shown in the figure, then which of the following statement is true? -~ / a PS @ scanned with OKEN Scanner(a) The time of flight is the same for all the three. (b) The launch speed is greatest for particle C. (c) The horizontal velocity component is greatest for particle C. (a) All of the above 52. Aprojectile is projected at an angle ot (> 45°) with an initial velocity u. The time (t) at which its vertical component of its velocity will be equal to the horizontal component of its velocity is (a) (cosa.— sina) ) 2 (eosa.+ sina) (4 (sina. — cos a) (2) sin? o— cos? a g 53 Abody has an initial velocity of 3 ms~* and has an acceleration of 1 ms~? normal to the direction of the initial velocity. Then its velocity, 4 s after the start is (a) 7 ms~ along the direction of initial velocity (b) 7 ms~* along the normal to the direction of the initial velocity {c)7 ms“ mid-way between the two directions (d) 5 ms~ at an angle of tan“* S with the direction of the initial velocity 54. Astone projected at an angle of 60° from the ground level strikes at an angle of 30° on the roof of a building of height h, then the speed of projection of the stone is ()2gh (o) Jégh (6) Jagh (a) gh 55 Aballis thrown eastward across level ground. A wind blows horizontally to the east and assume that the effect of wind is to provide is constant force to the east, equal in magnitude to the weight of the ball. The angle 6 (with respect to horizontal) at which the ball should be projected, so that it travels maximum horizontal distance is (a) 45° (b) 37° (253° (a) 67.5° 56 If 4s be the time in which a projectile reaches a point P of the its path and 5 s the time from P till it reaches the horizontal plane through the point of projection. The height of P above the horizontal plane will be [take, g =9.8 m/s?] (a) 98m (b) 49m (c) 196m (d) 147m 57 From the ground level, a ball is to be shot with a certain speed, Graph shows the range Rit will have versus the launch angle 6. The least speed the ball will have during its flight, if @ is chosen such that the flight time is half of its maximum possible value, is equal to (take, g=10m/s*) Rim) 250m 200m 100m ‘8(in degree) (a) 250 m/s (b) 50¥3 m/s (c) 50 m/s (d) 253 m/s @ scanned with OKEN Scanner58 5 Sy 61 63 65 66 A particle is projected from a horizontal floor with speed 10 m/s at an angle 20° with the flog, | and striking the floor after sometime. State which is correct. | (a) Velocity ct naricle will be perpendicular to initial direction two seconds after projection, | {b) Minimun: «need of particle will be 5 m/s, | (0) Displacement ot | (d) None of th A shot is fircc at an angle @ to the horizontal such that it strikes the hill while moving horizontally. “inc initial angle of projection 8. rticle after half second will be m, bs (a) tano=? tbytane=2 (C) tano=3 (d) None of these From the te... icwer, two balls are thrown horizontally with velocitiesu, and, in opposite directions. . then velocities are perpendicular to each other just before they strike the groung, then find the height of tower. o ng (o) Atty uu, 4g Two bodies are thrown simultaneously from the same point, One straight up and the other at an angle @ to the horizontal. The initial speed of each body is equal tou. The distance between the two besides t seconds later is (a)ut,/2(1 + sin @) (b) ut,/2{t = sin @) (c)ut,/2(1 + cot @) (qd) ./2uttt = sin @) A particle is projected speed 50 m/s at an angle of 53°, find out the time when velocity vector makes an angle of 83° with the initial vector. (as (b) 4+V3s ()4-V3s (d)4s A projectile is thrown with a speed v at an angle @ with the vertical. Its average velocity between the instants it crosses half the maximum height is (2) v sin },i-.cizontal and in the plane of projection (b) v co: @,orizontal and in the plane of projection (©) 2v sin@, horizontal and perpendicular to the plane of projection (d) 2v cos 6, vertical and in the plane of projection plane surface is inclined making an angle @ with the horizontal. From the bottom of this inclined piane, a bullet is fired with velocity v. The maximum possible range of the bullet on the inclined plane is, (a) (b) (a) v? v? v? {b) () (d) 8 a (i+sin@) g(1-sin@) g(t + cos 8) A baall is horizontally projected with a speed v from the top of a plane inclined at an angle 45° with ithe horizontal. How far from the point of projection will the ball strike the plane? a (o) 222 Qu ne 8 g g A particle is projected at angle 37° with the incline plane in upward direction - speed 10 m/s. The angle of incline plane is 53°, then the maximum distance from the incline plane attained by the particle will be (a)3m (b)4m (5m (d) zero @ scanned with OKEN Scanner67 6 8 69 70 Onan inclined plane of inclination 30°, a ball is thrown at an angle of 60° with the horizontal from the foot of the incline with a velocity of 10/3 ms“. If g = 10 ms’? then the time in which ball will hit the inclined plane is fa)is (b) 6s ()2s (d) 45 A projectile is fired at an angle @ with the horizontal. Find the condi perpendicular on an inclined plane of inclination a. as shown in figure. (b) cos a = sin (8 - ct) (d)2 tan o. = cot (0 - a) At what speed (in m/s) must a pebble be thrown at a height of h = 4.6 mand at an angle of 30° with the horizontal, iit is to hit the ground at angle of 45°? (a) mm/s, (b) 8 m/s (c) 10 m/s (d) 12 m/s A particle move along the parabolic path x =y? +2y +2 in such a way that the y-component of velocity vector remains 5 m/s during the motion. The magnitude of the acceleration of the particle is {a) 50 m/s? (€) 10V2 m/s? under which it lands {a) sino. = cos (@-a) (c) tan@ = cot (6~a) (b) 100 m/s? (d) 0.1 m/s? Numerical Value Questions nv & # a oa “N The speed of a particle when it is at its greatest height is ie imes of its speed when it is at its one-third of the maximum height. If the angle of projection is 2, then find the value of n. n Astone is thrown horizontally from a tower. In 0.5 s after the stone began to move, the Aumerical value of its velocity was 1.5 times its initial velocity. Ifthe initial velocity of stone is lp m/s, find the value of p. [Take, g = 10 m/s?] A bullet is fired with speed 50 m/s at 45° angle, find the height (in m) of the bullet when its direction of motion miakes angle 30° with the horizontal. [Take, g = 10 m/s] A ball is projected at an angle of 37° above with the horizontal from the top of a tower and strikes the ground in 7 s at an angle of 45° with the horizontal. Find the height (in m) of the tower. [Take,g = 10 m/s*] A projectile is thrown with speed u making angle @ with horizontal at t =0. It just crosses the two points at equal height at time t =1s andt =3 5s, respectively. Calculate maximum height attained by it. [Take,g = 10 m/s?] A building 7.5 m high and 2b meters wide has a flat roof, A ball is Projected from a point on the horizontal ground 28.4 m away from the building along its width. If projected with velocity 20 m/s at an angle of 45° with the ground, the ball hits the roof in the middle, find the width 2b (in m). (Take, g = 10 m/s?} A gun kept on a straight horizontal road is used to hit a car, travelling along the same road away from the gun with a uniform speed of 72 km/h, The car is at a distance of 120 m from the un , when the gun is fired at an angle of 37° with the horizontal. Find the speed (in m/s) of Projection of the shell from the gun. [Take, g = 10 m/s?] @ scanned with OKEN Scanner° 10 11 14 15 A particle is projected from point P with velocity 5/2 ms“ perpendicular to the surface of a hollow right angle cone whose axis is vertical. It collides at Q normally, find the time of the flight (in s) of the particle. iY c ‘Q So x A shell is fired from point O on the level ground with velocity 50 m/s at an angle 53°. A hill of uniform slope 37° starts from point A that is 100 m away from the point O as shown in the figure. Calculate the time of flight (in seconds). o A body is projected with speed 40/2 m/s at an angle of 45° with horizontal. If displacement of the particle in the 4th second is 5Vx, then find the value of x. A particle is projected with speed 30 m/s at angle of 22.5° with horizontal from ground as shown in figure. AB and CD are parallel to Y-axis and B is the highest point of trajectory of the Particle. Find the ratio of —. AB) A particle is projected from a point O with an initial speed of 30 m/s to pass through a point which is 40 m from O horizontally and 10 m above. There are two angles of projection with horizontal for which this is possible. If these angles are o and B, then find the value of tan [-{a +B}. A particle is projected upwards with a velocity of 100 m/s at an angle of 60° with the vertical. Find the time when the particle will move perpendicular to its initial direction. [Take, g =10 m/s?] : A ball is projected on smooth inclined plane in direction perpendicular to line of greatest slope with velocity of 8 m/s. Find its speed (in m/s) after 1s. sf p A projectile is fired into the air from the edge of a 100 m high cliff at angle of 37° above the horizontal. The projectile hits a target 400 m away from the base of the cliff. If initial velocity of the projectile vq is x5 m/s, then find the value of x. (Neglect air friction and assume X-axis to be horizontal and Y-axis to be vertical), @ scanned with OKEN Scanner46 Find range of projectile on the inclined plane which is projected perpendicular to the inclined plane with velocity 20 m/s as shown in figure. u=20ms" 37° 17 Aparticle starts from the origin at t = 0 and moves in the xy-plane with constant acceleration a in the y-direction. Its equation of motion is y = bx?. If the x component of its velocity is given by then calculate the value of n. nl 18 Ais the highest point on the path of a projectile and average velocity of the projectile between Oand Ais8i +3}. Iftan ais given bys, then calculate the value of n. 19 Acylinder is placed on a horizontal surface. A particle is projected with speed u and it crosses the cylinder by just touching it at two points as shown in figure. Then, the initial speed with which the mass projected is /5x m/s. Find the value of x. 20 Two diffs of height 120 m and 100.4 m are separated by a horizontal distance of 16m. Ifa car has to reach from the first cliff to the second, find the minimum horizontal velocity (in m/s) of car. @ scanned with OKEN ScannerLevel 2 Single Choice Correct Questions 1. (d) 2. (a) 3. (d) 4. (0) 5.(d) 6 (c) 7. (b) 11. () 42. (b) 13. (d) 14. (9) 15. (€) 16. (b) 17. (0) 21. (a) 22. (c) 23. (c) 24. (b) 25. (a) 26, (b) 27 (d) 8. (a) 9. (a) 10. (a) 18. (a) 19. (c) 20. (c) 28.(c) 29. (c) 30. (a) @ scanned with OKEN Scanner31. (d) 41. (b) 51. (d) 61. (b) 32. (b) 42. (c) 52. (c) 62. (b) 33. (a) 43. (c) 53. (d) 63. (b) 34, (c) 44. (a) 54. (c) 64. (b) 35. (b) 45. (c) 55. (d) 65. (d) 36..(b) 46. (a) 56. (a) 66. (a) 37. (a) 47. (c) 57. (d) 67. (c) 38. (a) 48. (c) 58. (a) 68. (d) 39. (a) 40. (c) 49. (b) 50. (d) 59. (c) 60. (a) 69. (b) 70. (a) @ scanned with OKEN Scanner