Question

A particle $P$ is projected from a point on the surface of a smooth inclined plane (see figure). Simultaneously another particle $Q$ is released on the smooth inclined plane from the same position. $P$ and $Q$ collide on the inclined plane after $t=4s$ . Find the speed of projection in $m{s}^{-1}$ . (take $g=10m{s}^{-2}$ )

Answer 1

Answer: 10

It can be observed from figure that $\text{P}$ and $\text{Q}$ shall collide if the initial component of velocity of $\text{P}$ and $\text{Q}$ on inclined plane i.e along incline should be equal. That is particle is projected perpendicular to incline.

$\therefore$ $\text{Time of flight T}=\frac{2{\text{u}}_{\perp }}{\text{ g}\text{ cos}\theta }=\frac{2\text{u}}{\text{ g}\text{ cos}\theta }$
$\therefore$ $\text{u}=\frac{\text{g}\text{T }\text{cos}\theta }{2}=10\text{ m}/\text{s}$