A ball with a mass of $5 kg$ is rolling at $12 m/s$ and elastically collides with a resting ball with a mass of $2 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2018-05-22T09:41:08

The velocities are $=5.14ms^-1$ and $=17.14ms^-1$

As the collision is elastic, there is conservation of momentum and conservation of kinetic energy.

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$1/2m_1u_1^2+1/2m_2u_2^21/2m_1v_1^2+1/2m_2v_2^2$

Threfore,

$5*12+2*0=5v_1+2v_2$

$5v_1+2v_2=60$ ............................ $(1)$

$1/2*5*12^2+1/2*2*0^2=1/2*5v_1^2+1/2*2v_2^2$

$5v_1^2+2v_2^2=720$ ......................... $(2)$

Solving for $v_1$ and $v_2$ in equations $(1)$ and $(2)$

${(5v_1+2v_2=60),(5v_1^2+2v_2^2=720):}$

$<=>$ , ${(v_2=1/2(60-5v_1)),(5v_1^2+2v_2^2=720):}$

$5v_1^2+2*(1/2(60-5v_1))^2=720$

$10v_1^2+3600-600v_1+25v_1^2=1440$

$35v_1^2-600v_1+2160=0$

$v_1=(600+-sqrt((-600)^2-4*35*2160))/(2*35)$

$=(600+-240)/70$

Therefore,

$v_1=12ms^-1$ or $v_1=5.14ms^-1$

$v_2=0ms^-1$ or $v_2=17.14ms^-1$

A ball with a mass of 5 kg 5 kg is rolling at 12 m/s12 m/s and elastically collides with a resting ball with a mass of 2 kg2 kg. What are the post-collision velocities of the balls?