An elastic ball is dropped on a long-inclined plane. If bounces, hits the plane again, bounces and so on. let us Label the distance between the point of the first and second hit d 12 and the distance between the points of second and the third hit is d 23 . find the ratio of d 12 /d 23 .
Text Solution
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If we rotate the coordinate system 80 that the ramp is horizontal then the free fall acceleration will have two components one downward a y = – g cos θ and one horizontal a x = g sin θ. In this frame, the initial velocity will have components given by V y = V 0 cos θ & V x = V 0 sin θ time for each bounce is given by t b = 
= 
The horizontal displacement
Δ x = V x t + 0.5 a x t 2
given these equation
d 12 = V 0 sin θ 
+ 0.5g sin θ 
= 
d 13 = V 0 sin θ 
+ 0.5 g sin θ 
= 
Since d 23 = d 13
d 12 = 
= 
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