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

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Question

$\begin{array}{l}
\,\,\,\,\,\,\,Here,\,{m_{1\,}} = m,{m_2} = 2m\
\,\,\,\,\,\,{u_1} = 2m/s,\,{u_2} = 0\
Coefficient\,of\,restitution,\,e = 0.5\

Vedclass · Accepted Answer

$0\;m/s,1\;m/s$

Vedclass · Answer

$\begin{array}{l}
\,\,\,\,\,\,\,Here,\,{m_{1\,}} = m,{m_2} = 2m\
\,\,\,\,\,\,{u_1} = 2m/s,\,{u_2} = 0\
Coefficient\,of\,restitution,\,e = 0.5\
Let\,{v_1}\,and\,{v_2}\,be\,their\,respective\,\
velocities\,after\,collision.\
Applying\,the\,law\,of\,conservation\,of\
linear\,momentum,\,we\,get\
\,\,\,\,\,\,\,\,\,\,\,\,\,{m_1}{u_1} + {m_2}{u_2} = {m_1}{v_1} + {m_2}{v_2}\
\,\,\,\,\,\,\,\,\,\,\,\,\,m 	imes 2 + 2m 	imes 0 = m 	imes {v_1} + 2m 	imes {v_2}
\end{array}$

$\begin{array}{l}
or\,\,2m = m{v_1} + 2m{v_2}\,or\,2 = \left( {{v_1} + 2{v_2}} ight)\,\,\,\,...\left( i ight)\
By\,definition\,of\,coefficient\,of\,restitution,\
\,\,\,\,\,\,\,\,\,\,\,\,e = \frac{{{v_2} - {v_1}}}{{{u_1} - {u_2}}}\
or\,\,\,\,\,\,\,e\left( {{u_1} - {u_2}} ight) = {v_2} - {v_1} \Rightarrow 0.5\,\left( {2 - 0} ight)\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {v_2} - {v_1}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} ight)\
Solving\,equations\,\left( i ight)\,and\,\left( {ii} ight),\,we\,get\
\,\,\,\,{v_1} = 0\,m/s,\,{v_2} = 1\,m/s
\end{array}$

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 after collision will be

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