A ball with a mass of $2 kg$ is rolling at $6 m/s$ 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 · 2017-09-01T07:13:45

The velocity of the first ball is $=-3.82ms^-1$
The velocity of the second ball is $=2.18ms^-1$

As the collision is elastic, we have conservation of linear momentum and conservation of kinetic energy.

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

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

so,

$2*6+9*0=2v_1+9v_2$ ,

$=>$ , $v_1=(12-9v_2)/(2)$ ........................ $(1)$

$1/2* 2*6^2+1/2*9*0=1/2*2*v_1^2+1/2*9*v_2^2$

$2v_1^2+9v_2^2=72$ .......................... $(2)$

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

$2*((12-9v_2)/(2))^2+9v_2^2=72$

$(12-9v_2)^2+18v_2^2=144$

$144-216v_2+81v_2^2+18v_2^2=144$

$v_2(99v_2-216)=0$

$v_2=0$ or $v_2=216/99=2.18ms^-1$

$v_1=1/2(12-9*2.18)=-3.82ms^-1$

A ball with a mass of 2 kg 2 kg is rolling at 6 m/s6 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?