Question

A body is thrown vertically upwards from point \(A\), the top of a tower, and reaches the ground in time \(t_1\). If it is thrown vertically downwards from \(A\) with the same speed, it reaches the ground in time \(t_2\). If it is allowed to fall freely from \(A\), the time it takes to reach the ground is given by:

• A. \(t=\dfrac{t_1+t_2}{2}\)
• B. \(t=\dfrac{t_1-t_2}{2}\)
• C. \(t=\sqrt{t_1t_2}\)
• D. \(t=\sqrt{\dfrac{t_1}{t_2}}\)

Hint:

For motion under gravity from the same height with equal speeds: \[ t_{\text{free fall}}=\sqrt{t_{\uparrow}t_{\downarrow}} \] This result is independent of initial speed.

Answer 1

The Correct Option is C