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