Q. A stone projected upwards with a velocity ‘u’ reaches two points ‘P’ and ‘Q’ separated by a distance ‘h’ with velocities u/2 and u/3. The maximum height reached by it is
(a) 9h/5
(b) 18h/5
(c) 36h/5
(d) 72h/5
Ans: (c)
Sol:
Maximum height reached is
$\displaystyle H = \frac{u^2}{2 g} $ …(i)
$ \displaystyle h = \frac{(u/2)^2 -(u/3)^2}{2 g} $
$\displaystyle h = \frac{5}{36} \frac{u^2}{2g}$
$\displaystyle h = \frac{5}{36}H $
Hence, H = (36/5)h