A ball of mass 1 kg moving with a velocity of 5 m/s collides elastically with rough ground at an angle $θ$ with the vertical as shown in Fig. What can be the minimum coefficient of friction if ball rebounds vertically after collision? (given $\tan θ = 2$ )

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answer is 1.

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Detailed Solution

From impulse–momentum theorem,

$\begin{array}{l} \int N d t = m (v + 5 \cos θ) ......... (i) \\ \int f d t = m 5 \sin θ \\ μ \int N d t = m 5 \sin θ ......... (i i) \\ \Rightarrow μ m (v + 5 \cos θ) = m 5 \sin θ \end{array}$

According to Newton’s law of restitution,
$v = e 5 \cos θ$
Solve to get $μ = 1$

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