Ball Bouncing on Ramp
There is a straight ramp which passes through the origin of the coordinate system and makes an angle of degrees with the positive axis. Gravity is in the negative direction.
A ball is released (starting at rest) from the point . Its first bounce off of the ramp occurs at the origin. How far away from the origin is the ball when it bounces for the third time?
Details and Assumptions: Bounces conserve the kinetic energy of the ball. A bounce multiplies the normal component of the velocity by negative one, and multiplies the tangential component by positive one.
Note:
This was inspired by a question posed by Azimuddin Sheikh. The drawing is not to-scale
The answer is 12.0.
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1 solution
Velocity of the ball just before striking the plane for the first time is u=√(20)m/s. Time elapsed between any two consecutive collisions is 2u/g. The distance between first and second collision points is 2u^2/g, and between the second and the third collision points is 4u^2/g. So the total distance is 6u^2/g=6(20)/10=12m.