A 30.0 kg cart travelling at 5.00 m/s collides with a 50.0 kg cart. Both carts immediately come to rest after the collision. What was the velocity of the 50.0 kg cart

30m/s

Explanation:

From the principle of conservation of momentum; it implies momentum before collision is same after collision hence

M1U1 + M2U2 = M1V1 + M2V1

Since both objects comes to rest after collision it means the final velocity is 0 and this has been represented as V1; hence the right side of the equation evaluates to zero.

We can then rewrite the equation as; M1U1 + M2U2=0

Let U1 and U2 be the respective velocity for M1 = 30kg and M2 = 50kg respectively.

Hence the equation becomes on substituting M1, M2 and U1.

We have;

30*5 + 50*U2 = 0

150 + 50U2=0

50U2 = - 150

U2 = - 150/50 = - 30m/s

Ignore the - ve sign which shows the direction of the 50kg mass was opposite that of 30kg