A ball with a mass of 5 kg is rolling at 9 m/s and elastically collides with a resting ball with a mass of 2 kg. What are the post-collision velocities of the balls?

1 Answer
Apr 8, 2017

The velocity of the first ball is =3.86ms^-1
The velocity of the second ball is =12.86ms^-1

Explanation:

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

m_1=5kg

m_2=2kg

u_1=9ms^-1

u_2=0ms^-1

Therefore,

v_1=3/7*9+4/7*(0)=27/7=3.86ms^-1

v_2=10/7*9-3/7*(0)=90/7=12.86ms^-1

Verificaition

m_1u_1+m_2u_2=5*9+2*0=45

m_1v_1+m_2v_2=5*3.86+2*12.86=45