Question

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

Answer 1

Answer: (C)

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

At $Q,{\left(\frac{u}{3}\right)}^2=u^2-2g{s}_2-(2)$

Maximum height $=\frac{u^2}{2g}-(3)$

$e{q}^n(2)-e{q}^n(1)\Rightarrow -2g(s_2-s_1)$ = $\frac{u^2}{9}-\frac{u^2}{4}$

$\Rightarrow +2gh=\frac{5u^2}{36}$

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

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