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question 23

A projectile is fired at an angleθ with the horizontal. Find the condition under which it lands perpendicular on an inclined plane inclination alpha as shown in figure.

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Solution for marked question:

Applying equation of motion perpendicular to the incline for y=0

0=Vsin(θ-a)t+1/2*(-gcosα)t2

⇒t=0&2Vsin(θ-α)/gcosα

At the moment of striking the plane, as velocity is perpendicular· to the inclined plane hence component of velocity along incline must be zero

0=vcos(θ-α)+(-gsinα)2Vsin(θ-α)/gcosα

vcos(θ-α)=tanα,2Vsin(θ-α)

cot(θ-α)=2tanα

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