A 3.0-kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0-kg cart that is initially moving to the left with a speed of 2.0 m/s. After the collision, the 3.0-kg cart is moving to the left with a speed of 1.0 m/s. What is the final velocity of the 5.0-kg cart?
A)zero m/s
B)0.80 m/s to the right
C)0.80 m/s to the left
D)2.0 m/s to the right
E)2.0 m/s to the left

Question

Quizplus · Accepted Answer

We can use conservation of momentum to solve this problem: 
Before the collision: 
Total momentum = (mass of cart 1 x velocity of cart 1) + (mass of cart 2 x velocity of cart 2) 
Total momentum = (3 kg x 1 m/s) + (5 kg x -2 m/s) 
Total momentum = -7 kg m/s (to the left)

After the collision: 
Total momentum = (mass of cart 1 x velocity of cart 1) + (mass of cart 2 x velocity of cart 2) 
Total momentum = (3 kg x -1 m/s) + (5 kg x v)  (where v is the final velocity of the 5-kg cart) 
Total momentum = -3 kg m/s + 5kg*v

Since momentum is conserved, we can set the before and after momenta equal to each other:

-7 kg m/s = -3 kg m/s + 5kg*v

Solving for v:

v = -0.8 m/s

So the final velocity of the 5-kg cart is 0.8 m/s to the left (since it was originally moving to the left with a velocity of 2 m/s, and the collision caused it to slow down). Therefore, the answer is C.

A 30-Kg Cart Moving to the Right with a Speed of of 1.0