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 $ms^{- 1}$ . (take $g=10ms^{- 2}$ )

Answer 1

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 $ $\text{Time of flight T} = \frac{2 \text{u}_{\bot}}{\text{ g} \text{ cos} \, \theta } = \frac{2 \text{u}}{\text{ g} \text{ cos} \, \theta }$
$\therefore $ $\text{u} = \frac{\text{g} \text{T } \text{cos} \, \theta }{2} = 1 0 \text{ m} / \text{s}$