A ball makes a head-on collision with another | vedclass

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(A) Let the mass of the first ball be $m_1 = m$ and the second ball be $m_2 = 2m$.The initial velocities are $u_1 = 1.5 \ m/s$ and $u_2 = 0 \ m/s$.The

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$-0.1 \ m/s$ and $0.8 \ m/s$

Vedclass · Answer

(A) Let the mass of the first ball be $m_1 = m$ and the second ball be $m_2 = 2m$.The initial velocities are $u_1 = 1.5 \ m/s$ and $u_2 = 0 \ m/s$.The coefficient of restitution is $e = 0.6$.The final velocity of the first ball is given by:$v_1 = \left( \frac{m_1 - e m_2}{m_1 + m_2} ight) u_1 = \left( \frac{m - 0.6(2m)}{m + 2m} ight) (1.5) = \left( \frac{1 - 1.2}{3} ight) (1.5) = \left( \frac{-0.2}{3} ight) (1.5) = -0.1 \ m/s$.The final velocity of the second ball is found using the definition of $e$:$e = \frac{v_2 - v_1}{u_1 - u_2} \Rightarrow 0.6 = \frac{v_2 - (-0.1)}{1.5 - 0} \Rightarrow 0.6 = \frac{v_2 + 0.1}{1.5}$.$v_2 + 0.1 = 0.6 	imes 1.5 = 0.9 \Rightarrow v_2 = 0.8 \ m/s$.Thus,the velocities are $-0.1 \ m/s$ and $0.8 \ m/s$.

$A$ ball makes a head-on collision with another ball of twice its mass,which is initially at rest,with a velocity of $1.5 \ m/s$. If the coefficient of restitution is $0.6$,what will be their velocities after the collision?

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