Question

A bumper car with mass m₁ = 115 kg is moving to the right with a velocity of v₁ = 4.8 m/s. A second bumper car with mass m₂ = 95 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?

2. What is the initial velocity of car 1 in the center-of-mass reference frame?

3. What is the final velocity of car 1 in the center-of-mass reference frame?

4. What is the final velocity of car 1 in the ground (original) reference frame?

5. What is the final velocity of car 2 in the ground (original) reference frame?

6. In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide.

What is the final speed of the two bumper cars after the collision?

ANSWER THIS QUESTION IN PARTICULAR PLEASE. DO NOT PROVIDE A GENERALIZED SOLUTION.

Answer 1

similar one but with different numericals sorry for the inconvenience

A bumper car with mass m1 = 110 kg is moving to the right with a velocity of v1 = 5 m/s. A second bumper car with mass m2 = 97 kg is moving to the left with a velocity of v2 = -3.9 m/s. The two cars have an elastic collision. Assume the surface is frictionless. (((Focus on #3. 1 and 2 are solved)))
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To understand this topic,

First do the problem in the usual ground (original) reference frame.

Lit us take u1 =5m/s and u2 = -3.9 m/s so that u refers initial. And final is denoted by v.
1 and 2 represent car 1 and car 2.

Momentum lost by car 1 = momentum gained by car 2.
110(5-v1) = 97(v2+3.9) -------------------1
v1= 1.561-0.882v2------------------1A

K.E lost by car 1 = K.E gained by car 2.
110(5^2-v1^2) = 97(v2^2 - 3.9 ^2) (after canceling 0.5 on both sides) --------------------2
Using (a^2