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If a ball is thrown vertically down with a velocity of 10m/s from a height of 3m. Find the maximum height it can reach after hitting the floor, if the coefficient of restitution is 0.7
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Coefficient of restitution (e) = 0.7

Before Rebound:-

$u = -10 m/s, s = -3, \\ a = -g = -9.81 m/s^3 $

Using, $v^2 = u^2 + 2as \\ \therefore v^2=(-10)^2 +2 \times -9.81 \times -3 \\ \therefore v^2=158.86 \\ \therefore v=12.6040 m/s$

Ball strikes the ground with a velocity of $12.604 m/s$

After Rebound:-

Velocity after first rebound $u_1 = ev = 0.7 \times 12.604 = 8.8228 m/s$

At highest point, $v_1 =0, a = -g = -9.81 m/s^2$ . Using,

$v_1^2=u_1^2+2as_1 \\ \therefore 0^2=(8.8228)^2 +2\times -9.81 \times s_1 \\ \therefore 19.62 s_1=77.8414 \\ \therefore s_1=3.9675 m$

Maximum height the ball can reach after hitting the floor $= 3.9675 m.$

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