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Gondola Car

How to solve these problems.?

We're asked to use this formula M1V1+M2V2=M1V1'+M2V2'. I'm having trouble identifying which would be the value for V1, V2, V1' and V2' and what to solve for. You don't need to solve for the problems, you can just give (or explain) the values for these variables.

1. A 60 kg skates travelling at 4 m/s overtakes a 100 kg skates travelling at 2 m/s in the same direction and collides with him. if two skates remain in contact, compute their final velocity.

2. If the skates in problem 1 are moving in opposite direction and collide then remain contact, what is their final velocity.

3. A 5 kg rifle fires a 0.25 kg bullet at a muzzle velocity of 500 m/s. Find the recoil velocity of the rifle.

4. A stationary refrigerator car with a mass 2x10^4 kg is rammed by a gondola car with mass 3x10^4 kg. before the impact the gondola car was going 1 m/s. If they lock together, what is the new velocity.

In every one of these problems two objects are locked together either before the collision ( the gun) of after the collision ( the others)
This reduces the number of variables.
So to take the first one.
After the collision they are locked together so v1' and v2' are the same.
Hence for the right hand side m1 v1' + m2 v2'
= (m1+m2) v1'
ie 60*4 + 100 * 2 = (60+100)v1' Which is easily soluble.

and for 2 60*4 + 100 * -2 = (60+100) * v1'

for the third the initial velocity is zero for both.
so ( 5+0.25)*0 = 0.25* 500 + 5 * v1'

And so on.

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LIONEL 6012 GONDOLA CAR
LIONEL 6012 GONDOLA CAR
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MTH 20 95138 O Union Pacific Gondola Car with ScaleTrax O 31 Switch 908309 9083
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MTH 30 72142 O American Steel Gondola Car with LCL Containers 2015
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30 72059 Railway Express Agency Gondola Car w LCL Containers 5969 MTH
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30 72151 Long Island Gondola Car w Crates MTH
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VINTAGE LIONEL 6142 GREEN GONDOLA CAR 1963 66 69 IN GOOD CONDITION
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