A ball with a mass of $3 kg$ is rolling at $5 m/s$ and elastically collides with a resting ball with a mass of $9 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2017-05-07T09:25:17

The velocity of the first ball is $=-2.5ms^-1$
The velocity of the second ball is $=2.5ms^-1$

In an elastic collision, we have conservation of momentum and conservation of kinetic energy

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

and

$1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2$

Solving the above 2 equations for $v_1$ and $v_2$ , we get

$v_1=(m_1-m_2)/(m_1+m_2)*u_1+(2m_2)/(m_1+m_2)*u_2$

and

$v_2=(2m_1)/(m_1+m_2)*u_1+(m_2-m_1)/(m_1+m_2)*u_2$

Taking the direction as positive $rarr^+$

$m_1=3kg$

$m_2=9kg$

$u_1=5ms^-1$

$u_2=0ms^-1$

Therefore,

$v_1=-6/12*5+18/12*(0)=27/7=-2.5ms^-1$

$v_2=6/12*5-6/12*(0)=90/7=2.5ms^-1$

Verificaition

$m_1u_1+m_2u_2=3*5+9*0=15$

$m_1v_1+m_2v_2=-3*2.5+9*2.5=6*2.5=15$

A ball with a mass of 3 kg 3 kg is rolling at 5 m/s5 m/s and elastically collides with a resting ball with a mass of 9 kg9 kg. What are the post-collision velocities of the balls?