Question

A body is projected vertically upwards. The times corresponding to height $h$ while ascending and while descending are $t_1$ and $t_2$ respectively. Then the velocity of projection is ($g$ is acceleration due to gravity).

• A. $g \sqrt {t_1 t_2}$
• B. $\frac {gt_1t_2}{t_1+t_2}$
• C. $\frac {\sqrt{gt_1t_2}} {2}$
• D. $\frac {g(t_1 + t_2)}{2}$

Answer 1

Answer: (D)

$\frac {g(t_1 + t_2)}{2}$

Answer 2

In case of motion under gravity, time taken to go up is equal to the time taken to fall down through the same distance.
Time of descent $\left(t_{2}\right)=$ time of ascent $\left(t_{1}\right)=\frac{u}{g}$
$\therefore$ Total time of flight $\quad T=t_{1}+t_{2}=\frac{2 u}{g}$
$\Rightarrow\,\,\,\,\,\,u=\frac{g\left(t_{1}+t_{2}\right)}{2}$