Question

A ball drops from a height of 2 meters. Each time it hits the ground, it bounces up 68 percent of the height it fall. Calculate the coefficient of restitution.

Answer 1

Coefficient of restitution is gvien by:

e = v/u = sqrt (2*g*h)/sqrt (2*g*H)

e = sqrt (h/H)

given that h = 68% of H

e = sqrt (0.68/1) = 0.825

derivation for coefficient of restitution

When ball is dropped from height H, then it's speed when it strikes the ground will be

V^2 = U^2 + 2*g*d

V = sqrt (2*g*H)

Now when it bounces off and again it hits the ground

V_new = sqrt (2*g*h)

gvien that h = 68% of H

So,

V_new = sqrt (2*g*0.68*H)

Now from definition of coefficient of restitution

e = V_new/V

e = sqrt (h/H)

e = sqrt 0.68 = 0.825

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