Rao

PRACTICE PROBLEMS
JEE- MAIN
Single answer choice type
hall is thrown from ground level so that itjust clears a wall 3 mhigh when it is moving horizontaly.
Q.1 Iftheinitial speed ofthe ball is 20 m/sthe angle of projection. [g=10m/s]
3 (B)cos-! 3
(A)sin-I (C) sin -!
V
20 V20 (D) cos
V10 V1
0.2
Anarticle is projected with a velocity of 10m/s at an angle of30° to the horizontal. Find its distance
from the point of projection 1/2 seconds later. [g= 10 m/s?]
Vi3 5V13 m
(A) m (B) (C) 2V13m (D)5/13 m
4 4

Q3 A particle is projected at an angle of 30° to the horizontal and 2seconds later is moving in the direction
tan- 1/4 to the horizontal for the first time its initial Speed. [g= 10 m/s]
160 110 160
m/s (B) -m/s
(A) (C) 4-V3 m/s (D) 130 m/s

Q4 Aparticle is projected from ground level with an initial velocity of 35 m/s at an angle of tan
3/4 to the horizontal. Find the time for which the particle is more than 2mabove the ground.
lg=10 m/s]
(A)6 sec (B) 4 sec (C) 3 sec (D) Isec
05 Two paticles are projected simultaneously from apoint Oin the same vertical plane with angles of
projection 30° and 60° and with the same initial speed of 2/3 m/s. Find the distance between them
after 2sec of their projection. [g= 10 m/s]
(A) 2/2(3 +V3) (B) V2(3-V3) (©) 23+ V3) (D) 2V2(3-V3)
0.6
Aballis projected with speed 20 m/s at an angle of 60° to the horizontal. Find also the height of the
Dall above the level ofthe point of projectionwhen it has travelled ahorizontal distance of 10 m.
lg=10 m/s}
(A) S(2V3 -1) (B) 10/3 (C) 5 (D) S(2V3 +1)
0.7 A
particle is projected with speed uat an angle of elevation a, where tana =3. Find,in tens of uand
3; lhe height of the particle when its speed is u/2.

(A) 3u (B) (C) (D)

8g 8g 8g
particle is projected from apoint Owhich is 100 mabove ground level. Theinitial velocityis
40 m/s horizontally. Findthetime at which the particle hits the ground.(p 10ms]
(A) J8 sec (B) V10 sec (O /20sec (D) 23 sec
 Kinemátics

thrown from the top ofatower which is ll mhigh and standsson horizontal \ground.emyThe
Q.9 Astoneis direction of motion is at 60 tothe
speed of projection is 12 m/s andthe initial
ground. [Take g =10m/s']
downward verical
Find the time taken for the stone toreach the
(B)1.8 s (C) 2.1 s (D) 2.4 s
(A) Is
Q.10 Aballrolls offthe top ofastaircase with a horizontal velocity u m/s. Ifthe steps are h metre high and
bmetre wide, the ball willhit the edge of thenth step, if
2hu 2hu' hu?
2hu (B) n= (C) n= (D) n=
(A) n=
gb
gb' gb
gb
JEE -ADVANCED
Single answer choice type
particle is projected from the ground with an initial speed ofv at an angle with horizontal. Th
A point of trajectoryis:
average velocity of theparticle between its point ofprojection and highest
(C) 2-V1+ 3cos'8
V
V

(A) ;V1+2cos' (B) ÷VI+cos' 8 (D) vcos

2
inclined at an angle o with the
VQ2 Particle A is released from a point P on a smooth inclined plane
Umaking an angle
horizontal. At the same instant another particle Bis projected with initial velocity
inclined plane. The relation between
B with the horizontal. Both the particles meet again on the
a and B is

(A) a+B= (B) a+B=

6 4

(C) a+B= 3 (D) a+G=

Bis t. Then the distance AB is equal

Q.3 In the figure, the time taken by theprojectile to reach from Ato
to
B

(A) (B) 2 60

A
(C) 3 ut (D) 2 ut
inclined at an angle with the
Q.4 Aprojectile is fired with avelocity uat right angles to the slope, which is
horizontal. The expression for the distance R to the point of impact is
2,2 2u
-sin cot 0 (B) tan sece
(A)

2u'-Tan '0 2u
R
-sin 20
(C) (D)
 Atruck is moving on ahhorizontal road with avelocity v =2im/s .Abody is projected with a velocity
Q.5
T4i+3j w.r.t. the truck. Horizontal range of the body w.r.t. a person on the ground is[g = 10 m

(A) 3.6m (B) 7.2 m (C) 2.4m (D) 1.2m

Aballis projected from apointA with some velocity at an angle 30 with the horizontal as
fgure. Consider a target pointB. The ball will hit the target if it is thrown with a velocityshown in the
Q.6
V, equal to
(A)Sm/s

(B) 6m/s 0.5m

(C) 7m/s -m

(D)Not possible for any finite value ofV,

Q.7 Aplane surface is inclined making an angle with the horizontal. From the bottom ofthis inclined
plane, a bullet is fired with velocity'v. The maximum possible range of the bullet on the inclined plane

(A) (B) (C) (D)

g(1+cos ) g(1+ sin ) g(1-sin )
Aparticle is projected with a certain velocity at an angle a above the horizontal from the foot of an
inclined plane of inclination 30°. Ifthe particle strikes the plane normally then ais equal to
2
(A) 30° + tan-! (B) 45° (C) 60° (D) 30°+tan-!R
2
Q.9 Aplane surface is inclined making an angle ß above the horizontal. Abullet is fired with the point of
projection at the bottom of theinclined plane with avelocity u, then the maximum range is given by
u u' u u'
(A) (B) (C) (D)
g(1+ sin B) g(l-sin B) g(1+ cosB)
Q.10 Aball is projected from point A witha velocity 10m/s perpendicular to the inclined plane as shown in
the figure. Range oftheball on the inclined plane is

30°

40 20 13 13
(A) m (B) 13 m (C) 20 m (D) m
40

Q1 Aparticle P is projected from a point on the surface ofsmooth inclined plane (see figure). Simulta
neously another particle Qis released on the smooth inclined plane from the same position. PandQ
collide after t= 4 second. The speed ofprojection ofP is

60°

(A) 5 mn/s (B) 10 m/s (C) 15m/s (D) 20m/s

 Q.12
horizontal. The distance xit will travel before again striking the slope is
ademy
Aball is projected with velocity uat right angle to the slope which is inclined at an angle a. with
hthe

2u 2u 2u tana 2u tan a.
(A) (B) tan a (C) gcos a
(D)
gsin
Q.13 Aparticle is projected with avelocity uin horizontal direction as shown in the figure. Find 'u' o
the particle collides orthogonally with the inclined plane of thefixed wedge.

Fixed
wedge

2gh 2gh 2gh

(A) v= (B)V= (C) v=
V4+cot'9 (D) none
V2+cot* 0 V2-cot0
One or more than one type
Q.14 Two particles are thrown from the samepoint in the same vertical plane, as shown in figure simultaneoust.
Then indicate the correct statements :

(A) Time of flight for B is less than that ofA (B)Projection speed ofB is greater than that ofA
(C) Horizontal component of velocityfor Bis greater than that ofA
throughout the duration for
(D) The vertical component ofvelocities ofboth Aand Bare always equal
which both the particles in air.
some velocity and with an acceleration Sm
Q.15 An aeroplane moving horizontally from west to east with
s drops a food packet at some instant. Then:
(A) The path of thepacket is parabolic with respect to ground
below the plane.
(B)Aperson sitting on the aeroplane shall see the packet is always vertically
angle tan(1/2) west ot
(C) With respect to plane, the packet travels in a stright line making an
vertical
angle tan(2) east of vertica
(D) With respect to plane, the packet travels in astright line making an
horizontal. The direction of velocity 01
Q.16 Abody is projected up with avelocity uat an angle with the further 1s, it reaches thS
the body makes angle 30 with the horizontal at t =2 s and then after
maximum height. Then [Take g= 10m/s]
(C) e= 45"
(D) =10/3m/s
(A) u=20/3m/s (B) = 60°
0.17 Twoinclined planes (I) and (Il) have inclination a and B respectively with horizontal, (where
a+ß=90") intersect each other at point Oas shown in figure. Aparticle is projected from point A
with velocity ualong adirection perpendicular to plane (). Ifhe particle strikes plane (ID
at B, then perpendicularly
(A) time of flight = u/g sin B
(B) time of flight =Wg sin a ()\ u (II)
(C) distance OB=u/2g sinß

(D) distance OB =u/2g sina

Q.18 Astone is project ed with a speed u at an angle x with directly aimed at a
monkey on a tree. As the
monkey sees the projection of stone monkey drops himselfvertically down
(A) Stone can never strike monkey (B) Stone can strike monkey
(C) Stone strikes monkey when monkey makes a vertical displacement of(1/2) gt
(D) Stonestirckes monkey when stone makes a vertical displacement of(1/2) gt
Q.19 Aboy is sitting in a car moving with uniform velocity. The boy throws a ball vertically upwards which
falls back into his hands. Aman standing on the road watches the motion of the ball. The path of the
motion ofthe ball will be
(A) a straight line for the man (B) a straight line for the boy
(C) a parabola for the man (D) a parabola for the boy
0.20 The co-ordinate of the particle in x-y plane are given as;
X=2+2t + 4t' and y= 4t + 8t The motion of the particle is :
(A) alonga straight line (B) unifomly accelerated
(C) along a parabolic path (D) nonuniformly accelerated
Q.21 Choose the correct alternative(s):
(A)Ifthe greatest height to which aman can throw astone is h, then the greatest horizontal distance
upto which he can throw the stone is 2h
(B) The angle ofprojection for aprojectile motion whoserange Risn times the maximum height His
tan'(4/n)
(C) The time of flight Tand the horizontalrange Rofa projectile are connected by the equation
gT²= 2Rtan where is the angle ofprojection
(D) Aball is thrown vertically up. Another ball is thrown at an angle 0 with the vertical. Both ofthem
remain in air for the same period of time. Then the ratio of heightsattained by the two balls is 1: 1.
Q.22 Aparticle is projected with speed of20 m/sec at 53° with horizontal att =0.(Consider g=10m/sec'):
20m/s
(A)Att=0.4sec it is moving at angle of45° with horizontal
53°
(B)at t=2.8 sec it is movingat angle of45° with horizontal
(C) the distance between the points where it make 45° with horizontal in 28.8 m
(D) speed ofthe particle at the point where it make 4$° with horizontal is l6.8 m/sec.
 Linked comprehension type emy
Passage -I

The trajectory of aprojectile in averticalplane is y=3 x-2x'. Ig=10 m/s ]

(x, y) P

Q.23 Angle of projection is

(A) 30° (B) 60° (C) 45° (D) /3 rad
Q.24 Maximum height His:
3
(A) 8/3 (B) (C) V3 (D) 2//3
Q.25 Range OA is :
V3 (C) \3 (D)8
(A) (B)
2 4
Q.26 Time of flight of theprojectile is:
3 10
(A) sec (B) V3 sec (C) 1sec (D) 2sec
V10
Passage -2
When a body is projected at an angle 9 from the horizontal, the path willbe parabolic. For the
parabolic path angle (0) between velocity and acceleration satisfies 0 <0< 180 with ÷0 or 180. f
0=90, then path ofthe particle is circular. If0 =0 or 180-’ then the path of the particle is astraight
line. In case projectile motion acceleration is constant but in the circular motion acceleration is variable.
In unifornm circular motiononly centripetal acceleration acts but in non uniform circular motion both
centripetal and tangential acceleration act.
X
Q.27 A particle in X-Y plane with y = and V, = 8-4t, the displacement versus time graph of the
particle would be :

(A) (B) (C) (D)

Q.28 The x andy coordinates ofa particle are x =A sin ot and y=Acos ot then the motion of the partice
is along
(A) acircle (B) an ellipse (C) a parabola (D) astraightline
Q.29 Aprojecile has the same maximum range Rfor two angles of projection , and 0, when pro)eu
with same speed. IfH, and H, are the maximum heights in two cases, then:
H H, H, H, =1
(A) H, = tan , (B) H, = tan ®, (C) H = cot O, (D) H,
 Passage-3
Aparticle is projected from Oand is moving freely under gravity and strikes the horizontalplane
through Oat adistance Rfrom it. Then.

OK
R
0.30 The maximum heightH and the range Rare related to each other as,
(A) R=4Hcot® (B)R =2Hcot (C)R=4Htan (D) R=2Htan
Q.31 The angle of elevation ofthe highest point of the projectile and the angle ofprojection are related
to each other as :

(A) tano - (tan0)2 (B) tano = (tan)4

(C) tano=2tan (D) tano=tan(/2)
VQ.32 In the figure, Band C are at the same level, the time difference between these two positions is t,,
A and Dare also at the same level, the time difference between these two positions is t,. Then t -t
is:

h
D

2h 4h 6h 8h
(A) (B) (C) (D)
Passage -4
Two inclined planes OA and OB having inclination (with horizontal) 30° and 60° respectively, intersect
each other at Oas shown in figure. Aparticle is projected from point Pwith velocity u = 10/3 ms
along a direction perpendicular to plane OA. If the particle strikes plane OB perpendicular at Q,
calculate

/B

30° 60°

Q.33 the velocity with which particle strikes the plane OB

(A)15m/s (B) 30m/s (C)20 m/s (D) 10 m/s
Q.34 Time of flight of the particle
(A)8 s (B)6s (C) 4 s (D) 2s
Q.35 The vertical height hof P from 0
(A) 10 m (B)5m (C) 15 m (D) 20 m
Q.36 The maximum height attained by the particle (from the line O)
(A) 20.5 m (B) 5 m (C) 16.25 m
Academy
(D) 11.25 m
Q.37 The distance PQ,
(A) 20 mn (B) 10 m (C) 5 m (D)2.5 m
Matrix match type
Q.38 For aprojectile, projected up from the ground, match the following two columns.
Column Icontains some physical quantities and columnIIcontains nature of their variations.
motion until it reaches the ground. during its
Column-I Column-II
(A)Tangential acceleration (p) First increases and then decreases
(B) Normal acceleration (q) First decreases and then increases
(C) Change in velocity in any time interval (r) Constant in direction
(D) Instantaneous velocity (s)Variable in direction
Q.39 A ballis projected horizontally with a speed of9.8 m/s from the top a tower of height 4.9 m. Then
match the following two columns.
Column-I Column-II
(A) Time of flight in seconds (p) 4.9
(B) Magnitude ofvelocity in m/s on reaching the () 9.8
ground
(C) Horizontal range in meters (r) 9.8V2

(D)Magnitude of change in vertical velocity in ,S in m/s (s) 1

Integer type
Q.40 Abody is thrown with the velocity v,at an angle of e tothe horizon. Determine v, ifthe maximum
height attained by the body is 2.5 mand at the highest point ofits trajectory the radius of curvatureis
r=3m. Neglect air resistance. [use V80 as9]
Q.41 x= 401 y=201-10r represent the equations governing motion of projectile on a planet. x and y
are expressed in meters. Time offlight on that planet is seconds

Q.42 Aground to ground projectile projected at t =0is at points Aat t = T , Is at point Bat t = 5T and
3 6

reaches the ground at (=T. The difference in heights between points Aand B is where K =
6K
Q.43 Aprojectile is projected from a point at the foot ofa fixed inclined plane having angle of
inclination
45', at an angle with horizontal. The particle hits the inclined plane at right
angles, if tan=