Question

A stone projected upwards with a velocity u reaches two points P and Q separated by a distance $h$ with velocities $\frac{u}{2}$ and $\frac{u}{3}$. The maximum height reached by it is

• A. $\frac{9h}{5}$
• B. $\frac{18h}{5}$
• C. $\frac{36h}{5}$
• D. $\frac{72h}{5}$

Answer 1

The correct option is C $\frac{36h}{5}$

At $P,(\frac{u}{2}{)}^2=u^2-2g{s}_1-(1)$

At $Q,(\frac{u}{3}{)}^2=u^2-2g{s}_2-(2)$
Maximum height $=\frac{u^2}{2g}-\left(3\right)$
$e{q}^n\left(2\right)-e{q}^n\left(1\right)\Rightarrow -2g(s_2-s_1)=\frac{u^2}{9}-\frac{u^2}{4}$
$\Rightarrow +2gh=\frac{5u^2}{36}$

$\Rightarrow \frac{36}{5}h=\frac{u^2}{2g}\to$ from $e{q}^n\left(3\right)$

Max ht $=\frac{36h}{5}$