Given below are two statements. One is labelled as Assertion (A) and the other is labelled as reason (R).
Body projected vertically up or down from the top of a tower with same velocity will reach the ground with same velocity.
Both the bodies projected vertically up and down from the top of the tower will have same displacement and acceleration.
In the light of the given statements, choose the correct answer from the options given. 

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(A) is true but (R) is false

Both (A) and (R) are true but (R) is not the correct explanation of (A)

Both (A) and (R) are true and (R) is the correct explanation of (A)

Both (A) and (R) are false

answer is A.

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Detailed Solution

Body projected vertically up or down from the top of a tower with same velocity will reach the ground with same velocity. Both of the bodies are moving under same acceleration, which is acceleration due to gravity. As the bodies finally come to the earth surface, the displacement of both the bodies will be same.

According to the equation, $v^{2} - u^{2} = 2 gh$

The final velocity is only dependent on the displacement and the acceleration of the bodies. So we can conclude that both of the bodies will have same velocity on reaching the ground. Therefore, both the statements are true and assertion is true because displacement and acceleration are the same for both cases.

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