question_answer

A particle P is projected from a point on the surface of 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 \[t=4\] second. The speed of projection of P is

A) 5 m/s   

B)        10 m/s

C) 15 m/s  

D)        20 m/s

Correct Answer: B

Solution :

[b]

It can be observed from figure that P and Q shall collide if the initial component of velocity of P on inclined plane i.e., along incline \[{{u}_{\,\text{I}\,\text{I}}}=0\] that is particle is projected perpendicular to incline.

Time of flight on an inclined plane of inclination \[\alpha \] is given by

\[\text{T=}\frac{2\text{u sin}\left( \theta -\alpha  \right)}{\text{g}\cos \alpha }\]

\[\Rightarrow 4=\frac{2\text{u sin90}{}^\circ }{10\times \frac{1}{2}}\Rightarrow \text{u= 10 m/s}\].