Question

If two cart(total mass =3m) “explode” from one another such that one cart (mass=m) moves away with velocity v, what velocity will the second cart (mass=2m) have?

Answer 1

The second cart with mass 2m will move with a velocity of -v / 2, opposite to the direction of the first cart due to conservation of momentum.

Step-by-step explanation:

The question involves a scenario where two carts with a combined mass of 3m explode from one another. One cart with mass m moves with velocity v, and we need to find out the velocity of the second cart with mass 2m. The law of conservation of momentum applies here, and it states that the total momentum before the explosion must equal the total momentum after the explosion.

Using conservation of momentum:

• Initial total momentum = Final total momentum
• 0 = m*v + 2m*v'

The 'v' represents the velocity of the first cart, and 'v'' stands for the velocity of the second cart after the explosion. To find 'v', we rearrange the formula as follows:

• 2m*v' = -m*v
• v' = -(m*v) / (2m)
• v' = -v / 2

Therefore, the second cart will move with a velocity of -v / 2, which means it will move in the opposite direction at half the speed of the first cart.