A particle is projected from the bottom of an inclined plane at an angle θ with the surface of the incline.The angle of the inclined plane is 45.For what value of θ will the particle retrace it's path after collision with the plane? Assume that the collision is ELASTIC.
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2 Answers
1161For now take a hint: For retracing the path, particle should strike the inclined plane normally (Why?). The answer for this question should be: θ=tan-1 (1/2).
Sushovan Halder yes sir.
Upvote·0· Reply ·2014-06-17 09:33:30- Akash Anand @Shushovan.. did you able to do that? If yes then try to post the solution.
263Let's consider that the particle did not hit the inclined plane normally.So it must have some horizontal and vertical velocity.Since the collision is elastic so after striking the plane it would have the same horizontal and vertical velocity,i.e. it would have some velocity up the incline.In that case the particle would have never retraced back it's path.It would have bounced upwards.So the only possibility is to hit the plane normally.
Then ,u*cosθ=(gsin45)*t............(1)[no horizontal velocity while striking].
u*sinθ=(gcos45)*(t/2)...............(2)[at the uppermost point of it's flight vertical velocity is 0].
Now,dividing we get cotθ=2.
NOTE:Here horizontal and vertical velocities are with respect to the inclined plane.
- Akash Anand Good work.