A ball moving with velocity 2 ,m/s collides h | vedclass

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Question

(A) Let the mass of the first ball be $m_1 = m$ and the mass of the second ball be $m_2 = 2m$.Initial velocities are $u_1 = 2 \,m/s$ and $u_2 = 0 \,m/

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(A) Let the mass of the first ball be $m_1 = m$ and the mass of the second ball be $m_2 = 2m$.Initial velocities are $u_1 = 2 \,m/s$ and $u_2 = 0 \,m/s$.The coefficient of restitution is $e = 0.5$.The velocity of the first ball after collision is given by $v_1 = \frac{(m_1 - em_2)u_1 + (1 + e)m_2u_2}{m_1 + m_2}$.Substituting the values: $v_1 = \frac{(m - 0.5 	imes 2m)(2) + (1 + 0.5)(2m)(0)}{m + 2m} = \frac{(m - m)(2) + 0}{3m} = 0 \,m/s$.The velocity of the second ball after collision is given by $v_2 = \frac{(m_2 - em_1)u_2 + (1 + e)m_1u_1}{m_1 + m_2}$.Substituting the values: $v_2 = \frac{(2m - 0.5 	imes m)(0) + (1 + 0.5)(m)(2)}{m + 2m} = \frac{0 + (1.5)(2m)}{3m} = \frac{3m}{3m} = 1 \,m/s$.Thus, their velocities after collision are $0 \,m/s$ and $1 \,m/s$.

$A$ ball moving with velocity $2 \,m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be:

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