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Question

A ball is shot vertically upward from the surface of another planet. A plot of 'y' versus 't' for the ball is shown in figure where y is the height of the ball above its starting point and t = 0 at the instant the ball is shot. The figure's vertical scaling is set by ys = 30.0 m. What are the magnitudes of (a) the free-fall acceleration on the planet and (b) the initial velocity of the ball?


A

a = - 8 m/, u = + 20 m/s

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B

a = 8 m/, u = + 20 m/s

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C

a = - g m/, u = + 22.5 m/s

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D

a = - 10/, u = + 25 m/s

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Solution

The correct option is A

a = - 8 m/, u = + 20 m/s


Given ys= 30. From graph maximum height = 25 m

Total time of flights of ball = 5 sec

Let the Ball be thrown with velocity u

When ball reaches the highest point velocity = 0

v = u + at

0 = u - at , t=ua

The ball will take same time to fall from that point

So the total time of flight = 2ua = 5

ua=52 u=5a2 .....(1)

Also s=ut+12at2

2su52+12(a)(52)2

Subtracting equation (1)

25=254a254a

25=258a

a = 8 m/s2 in down ward as we already assumed a to be downward and solved 80

a = - 8m/s2

u = 20 m/s


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