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Projectile Motion - 1 PDF

Two particles are projected at different angles from the same point with the same speed. Their times of flight are different but their horizontal ranges are the same. This can only occur if the sum of the angles is 90 degrees. The velocity of a particle moving along the path y=x^2/2 at t=2 seconds is 5 m/s. If two projectile paths have the same range R, then the range is proportional to the square root of the product of their greatest heights h and h'. When a particle is thrown horizontally, the resultant velocity at any time t is the square root of the initial velocity squared plus the acceleration due to gravity squared times t squared.

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Ramesh Badam
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363 views2 pages

Projectile Motion - 1 PDF

Two particles are projected at different angles from the same point with the same speed. Their times of flight are different but their horizontal ranges are the same. This can only occur if the sum of the angles is 90 degrees. The velocity of a particle moving along the path y=x^2/2 at t=2 seconds is 5 m/s. If two projectile paths have the same range R, then the range is proportional to the square root of the product of their greatest heights h and h'. When a particle is thrown horizontally, the resultant velocity at any time t is the square root of the initial velocity squared plus the acceleration due to gravity squared times t squared.

Uploaded by

Ramesh Badam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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EXERCISE-III

Q.l Two particles are projected from the same point with the same speed, .at different angles 8 1 and
O2 to the horizontal. They have the same horizontal range. Their times of flight are tl and ~
respectively :­

(1) 0 1 + 92 = 900 (2) -' = tanO (3)


t1
-= tan 0 t1 --.!L
t2 I t2 2 (4) sin9i - sin92

2 2
Q.2 A particle moves along the positive branch of the curve y = x where x = ~ , where x and y
2

are measured in metre and t in second. At t = 2 sec, the velocity of the particle is :­

(1) (21-41) mlsec (2) (21+4]) mlsec (3) (21 +21) mlsec (4) (41 -2]) mlsec

Q.3 A cannon ball has a range R on a horizontal plane. If h and h' are the greatest h~ights in the two
paths for which this is possible, then :­

(1) R = 4 .j(hh') (2) R = 4h (3) R = 4 h h' (4) R JW


h'

QA When a particle is thrown horizontally, the resultant velocity of the projectile at any time t is
given by :­

(1)gt (2) igt2 (3) Ju2 +g2 t 2 (4) Ju2 g2 t 2

Q.5 A particle is thrown with a speed u at an angle 8 with the horizontal. When the particle makes an.
angle ~ with the horizontal, its speed changes to v :­
(1) v = ucos 0 (2) v = ucosO . cos~

(3) v = ucosO . sec~ (4) v = usecO . cos~

Q.6 If retardation produced by air resistances to projectile is one-tenth of acceleration due to gravity,
the time to reach maximum height approximately :­
(1) increase by 9% (2) decrease by 9% (3) increase by 11% (4) decrease by 11%

Q.7 Find the average velocity of a projectile between the instants it crosses half the maximum height.
It is projected with a speed u at an angle 0 with the horizontal :­

(1) u cos 0 (2) u sin 0 (3) u (4) u'tan 0

Q.8 A particle starts from the origin of coordinates at time t 0 and moves in the xy plane with a
constant acceleration ex. in the y-direction. Its equation of motion is y := px2• Its velocity
component in the x-direction is :- .

(1) variable (2)


~
VP
a
(3) 2P (4) Hi
AssertiorilReason Type Questions:
Q.9 Statement-I: Two balls ofdifferent masses are thrown verticallyup with same speed. They will pass
through their point· ofproj ection in downward direction with the same speed.
Statement-2: The maximum height and downward velocity attained at the point ofprojection are
independent ofthe mass ofthe ball.
,(1) Ifboth Statement-I and Statement-2 are true, and Statement-2 is the correct explanation of
Statement-I.
(2) If both Statement-l and Statement-2 are true but Statement-2 is not the correct explanation of
Statement-I.
(3) If Statement-I is true but Statemeht-2 is false.
(4) If Statement-I is false but Statement-2 is true.

Q.IO Statement-I: Forangle ofprojectiontan-I (4), the horizontal range and maximum height are equal.

Statement 2 : The maximum range ofprojectile is directly proportional to square of velocity and

inversely proportional to accelemtion ofgmvity.

(1) Ifboth Statement-I and Statement-2 are true, and Statement-2 is the correct explanation of
Statement-I.
(2) If both Statement-I and Statement-2 are true but Statement-2 is not the correct explanation of
Statement-I .

. (3) If Statement-I is true but Statement-2 is false.

(4) If Statement-I is false but Statement-2 is true.

Column matching Type Question:


, 2
Q.l1 Trajectory ofparticle in a projectile motion is given as: y = x - x . Here, x and y are in metres. For
80 .

this projectile motion match the followingwithg= i 0 mls2·


Column-J Column-ll
(A) Angle ofprojection (p)20m
(B)Angle ofvelocitywith (Q)80m
~

horizontal after 4s
(C) Maximum height (R)45°

(D) Horizontal range (S)tan- l (~),

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