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Question

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 after $$t = 4s$$. The speed of projection of P is:-
1029088_5f25d0bd6cf94ea8837bb2e34315fe9d.png


A
5 m/s
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B
10 m/s
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C
15 m/s
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D
20 m/s
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Solution

The correct option is B 10 m/s
Relative velocity of a particle P in the frame of Q changes linearly with time during the flight of P
Acceleration of Particle P and Q along the inclined is same
Acceleration of particle P perpendicular to the incline plane $$=10\ cos60$$
                                                                                                     $$=10\times\dfrac{1}{2}$$
                                                                                                     $$=5\ m/sec^2$$
So,
$$\Rightarrow V_P-5(2)=0$$
$$\therefore V_P=10\ m/sec$$
Hence speed of projection of P is 10 m/sec.

Physics

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