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?

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Solution

The correct option is **A**

a = - 8 m/s^{2}, 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/s^{2} in down ward as we already assumed a to be downward and solved 80

a = - 8m/s^{2}

u = 20 m/s

0

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