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/s2, u = + 20 m/s

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B

a = 8 m/s2, u = + 20 m/s

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C

a = - g m/s2, u = + 22.5 m/s

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D

a = - 10/s2, u = + 25 m/s

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Solution

## The correct option is A a = - 8 m/s2, 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 2s−u52+12(−a)(52)2 Subtracting equation (1) 25=254a−254a 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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