A bumper car with mass m 1 = 115 kg is moving to the right with a velocity of v

Question

A bumper car with mass m1 = 115 kg is moving to the right with a velocity of v1 = 4.9 m/s. A second bumper car with mass m2 = 96 kg is moving to the left with a velocity of v2 = -3.8 m/s. The two cars have an elastic collision. Assume the surface is frictionless.

1) What is the velocity of the center of mass of the system?    .94 m/s

2)What is the initial velocity of car 1 in the center-of-mass reference frame?   3.90 m/s

I need help with:

What is the final velocity of car 1 in the center-of-mass reference frame? and What is the final velocity of car 1 in the ground (original) reference frame?

Explanation / Answer

m1 = 115 kg
v1 = 4.9 m/s

m2 = 96 Kg
v2 = -3.8 m/s

Using Momentum Conservtaion,
m1v1 + m2*v2 = m1*v1f + m2*v2f
115*4.9 - 96*3.8 = 115*v1f + 96*v2f ------1

Using Energy Conservtaion,
1/2*m1v1^2 + 1/2*m2*v2^2 = 1/2*m1*v1f^2 + 1/2*m2*v2f^2
115*4.9^2 + 96*3.8^2 = 115*vif^2 + 96*v2f^2 ------2

Solving eq 1 & 2,
v1f = -3.0 m/s
v2f = 5.7 m/s

Final velocity of car 1,
Center-of-mass reference frame, = -3.0 - 0.94
Center-of-mass reference frame, = - 3.94 m/s
ground (original) reference frame, = -3.0 m/s

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