Q. 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) $\frac{gt_{1}t_{2}}{t_{1} + t_{2}}$
C) $\frac{g\ \sqrt{t_{1}t_{2}}}{2}$
D) $\frac{g\left( t_{1} + t_{2} \right)}{2}$
Explanation
(d) In case of motion under gravity, time taken to go up is equal to the time taken to fall down through the same distance.
$Time\ of\ desent\left( t_{2} \right) = \ time\ of\ ascent\left( t_{1} \right) = \frac{u}{g}$
$\therefore Total\ time\ of\ flight\ \ T = t_{1} + t_{2} = \frac{2u}{g}$
Or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ u = \frac{g\left( t_{1} + t_{2} \right)}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.