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Question

If h1,h2 and h3 are the displacements of object along the incline plane between 1st2nd,2nd3rd and 3rd4th impact, then h1:h2:h3.

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Solution

R.E.F image
Suppose the object coincides at a velocity
V in the 1st impact.
Considering t challenges a projective motion the
velocity before the 2ndconcision is V as were.
Suppose, the coefficient of restitution =e
Where, e<1 (for non - elastic concision)
The velocity after 2nd concision is ev
and 3rd collision is e2v
Let the angle of inclined power be θ
Vertical component of velocity after
1st concision is vcosθ
2nd concision is evcosθ
3rd concision is e2vcosθ
12m(vcosθ)2=mgh1
h1=(vcosθ)22g
h2=(evcosθ)22g
h3=(e2vcosθ)22g
h1:h2:h3=1:e2:e4

1115106_806166_ans_e3c4542fe9c644c8bf40faf9bcaa630f.jpg

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