A ball moving with velocity $5 \mathrm{~m} / \mathrm{s}$ collides head on with another stationary ba

Question

A ball moving with velocity $5 \mathrm{~m} / \mathrm{s}$ collides head on with another stationary ball of three times the mass. If the coefficient of restitution is $0.4$, then their velocities (in $\mathrm{m} / \mathrm{s}$ ) after collision will be\

Professor PC Thomas Classes · Answer

(c) : $m_1=m, m_2=3m, u_1=5, u_2=0, e=0.4$. COM: $m(5) = m v_{1} + 3m v_{2} \implies 5 = v_{1} + 3 v_{2}$ (1). COR: $0.4 = \frac{v_{2}-v_{1}}{5-0} \implies v_{2} = v_{1} + 2$ (2). Substitute (2) into (1): $5 = v_{1} + 3(v_{1} + 2) \implies 4v_{1} = -1 \implies v_{1} = -0.25 \mathrm{~m} / \mathrm{s}$. $v_{2} = -0.25 + 2 = 1.75 \mathrm{~m} / \mathrm{s}$.