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Question

A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) The maximum height to which it rises.
(ii) The total time it takes to return to the surface of the earth.

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Solution

Given Initial velocity of ball, u=49 m/s

Let the maximum height reached and time taken to reach that height be H and t respectively.
Assumption: g=9.8 m/s2 holds true (maximum height reached is small compared to the radius of the earth)

Velocity of the ball at maximum height is zero, v=0
Using the third equation of motion we get,
v2u2=2aH
0(49)2=2×(9.8)×H
H=122.5 m
Using the first equation of motion we get,
v=u+at
0=499.8t
t=5 s
Total time taken by ball to return to the surface, T=2t=10 s.

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