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 = 8 seconds at some point on the inclined plane. Then find the speed of projection of P in m/s. $(g = 10 m / s^{2})$

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answer is 20.

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Detailed Solution

It can be observed from figure that P and Q shall collide if the initial component of velocity of P along incline. $u_{| |} = 0$ that is particle is projected perpendicular to incline.

$∴ Time of flight T = \frac{2 u_{⊥}}{g \cos θ} = \frac{2 u}{g \cos θ} ∴ u = \frac{g T \cos θ}{2} = 20 m / s .$

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