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Question

A ball is projected down the incline plane with velocity u at right angle to the plane which is inclined at an angle α with the horizontal. The distance x along the inclined plane that it will travel before again striking the slope is 
  1. 2u2gcosα
  2. 2u2gtanα
  3. 2u2gtanαcosα
  4. 2u2gtanαsinα


Solution

The correct option is C 2u2gtanαcosα

We know that range of a projectile down an incline plane is given by
R=u2gcos2α[sin(2θ+α)+sinα] (where θ is the angle of projection with the horizontal and α is the angle of inclination of the plane)
Here θ=90α and angle of inclination = α
x=u2gcos2α[sin(2(90a)+α)+sinα]=2u2sinαgcos2a=2u2gtanαcosα

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