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# momentum/ relativity? watch

1. Imagine two passengers (each having the same mass m) are standing atop an empty flat train car of mass M, initially at rest on a frictionless track. Both passengers will jump off the cart in the same direction with a speed Vp relative to the cart, but in two different sequences.

I) Find the final speed of the cart if both passengers jump off the train at the same instant.

II) Find the final speed of the cart if one passenger jumps off, then the second passenger jumps off (not simultaneous)

III) In which of these two cases does the cart wind up with the greater speed, or does it not matter?

Can anyone please explain to me the ways to approach this question? I understand the basic concept behind relativity but whenever there is a question I don't know where to start :'( !!!

The answer for I) is Vec (velocity of cart relative to the earth) = 2m(Vp)/(M+2m). How is this so?
2. (Original post by liemluji)
Imagine two passengers (each having the same mass m) are standing atop an empty flat train car of mass M, initially at rest on a frictionless track. Both passengers will jump off the cart in the same direction with a speed Vp relative to the cart, but in two different sequences.

I) Find the final speed of the cart if both passengers jump off the train at the same instant.

II) Find the final speed of the cart if one passenger jumps off, then the second passenger jumps off (not simultaneous)

III) In which of these two cases does the cart wind up with the greater speed, or does it not matter?

Can anyone please explain to me the ways to approach this question? I understand the basic concept behind relativity but whenever there is a question I don't know where to start :'( !!!

The answer for I) is Vec (velocity of cart relative to the earth) = 2m(Vp)/(M+2m). How is this so?
If Vp is the velocity of m relative to the cart, what is it's velocity relative to the Earth? (It's not Vp). And take it from there.
3. (Original post by ghostwalker)
If Vp is the velocity of m relative to the cart, what is it's velocity relative to the Earth? (It's not Vp). And take it from there.
So Vep(m relative to earth)= Vec(cart relative to earth)+ Vcp(m relative to cart)

and Vcp is equivalent to Vp and how do I take on from here?
4. (Original post by liemluji)
So Vep(m relative to earth)= Vec(cart relative to earth)+ Vcp(m relative to cart)

and Vcp is equivalent to Vp and how do I take on from here?
Conservation of momentum, in Earth frame.

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