Please be legible on paper(if provided) and please explain the reasoning behind

Question

Please be legible on paper(if provided) and please explain the reasoning behind each steps.

When a ball bounces on the ground, the height of each successive bounce decreases because during each bounce, some kinetic energy is converted to thermal energy; that is, in an inelastic collision. Delta Eth 0. Consequently, mechanical energy is not conserved: DeltaEmec 0. As discussed in lecture, the coefficient of restitution is the ratio of speeds immediately before and after the bounce: Cr = vf /vi. Use this fact as well as energy considerations to show that it also may be given by the square root of the ratio of the maximum heights attained before and after the bounce: . (Note: The PGA rule on drivers is CR 83)

Explanation / Answer

before bounce :

suppose it comes from hi height and have vi velocity jus before collision,

the using energy conservation ,

mghi = mvi^2 /2

vi = sqrt(2ghi)

after bounce:

it have velocity vf and suppose will to hf height then using energy conservation,

mvf^2 /2 = mghf

vf = sqrt(2ghf)

as given ,

cR = vf/ vi = sqrt(2ghf) / sqrt(2ghi) = sqrt(hf/hi)

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