A ball with a mass of 2 kg2kg is rolling at 1 m/s1ms and elastically collides with a resting ball with a mass of 3 kg3kg. What are the post-collision velocities of the balls?

1 Answer
Apr 25, 2016

u_1=-1/5 m/su1=15ms
u_2=4/5 m/su2=45ms

Explanation:

"given data:"given data:
m_1=2kgm1=2kg
v_1=1m/sv1=1ms
"Momentum before collision for the first ball:"Momentum before collision for the first ball:
vec P_1=m_1*v_1=2*1=2 kg*m/sP1=m1v1=21=2kgms

m_2=3 kgm2=3kg
v_2=0v2=0
"momentum before collision for the second ball:"momentum before collision for the second ball:
vec P_2=3*0=0P2=30=0

"Total momentum before collision:"Total momentum before collision:
vec P_b=vec P_1+vec P_2Pb=P1+P2
vecP_b=2+0=2 kg*m/sPb=2+0=2kgms

"Velocities for post collision :"Velocities for post collision :

u_1:"Post collision velocity of the first ball"u1:Post collision velocity of the first ball

u_1=(2*vec P_b)/(m_1+m_2)-v_1u1=2Pbm1+m2v1

u_1=(2*2)/(2+3)-1u1=222+31

u_1=4/5-1u1=451

u_1=-1/5 m/su1=15ms

u_2:"Post collision velocity of the second ball"u2:Post collision velocity of the second ball

u_2=(2*vec P_b)/(m_1+m_2)-v_2u2=2Pbm1+m2v2

u_2=(2*2)/(2+3)-0u2=222+30

u_2=4/5 m/su2=45ms