Question

a 10-kg cart moving to the right at 5 m/s has a head-on collision with a 5-kg cart moving to the left at 7 m/s. if the carts stick together, what is the velocity of the combination?

Answer 1

1 m/s (to the right)

Step-by-step explanation:

`mv_(1) + mv_(2) = m_(total)v_(final)\\\\10*5 + 5*(-7 )= (10+5)v_(final)\\ \\50 - 35 = 15*v_(final)\\\\v_(final)= 15 / 15 \\\\v_(final)=1 m/s`

Notice that we have a negative value for the velocity of the second cart. This is because the cart is moving to the left and we took right to be our positive direction. Velocity is a vector, so the direction matters. If we had taken left to be our positive direction, the answer would be v= - 1m/s which would still mean that the combination moves to the right.