Question

A small 300 g cart moves at 1.80 m/s on a frictionless track and collides with a larger 1.00 kg cart at rest. After the collision, the small cart recoils at 0.810 m/s. What is the velocity of the larger cart after the collision?

a) 0.180 m/s
b) 0.810 m/s
c) 1.080 m/s
d) 1.620 m/s

Answer 1

The velocity of the larger cart after the collision is 0.18 m/s.

Step-by-step explanation:

When two objects collide, their total momentum before the collision is equal to their total momentum after the collision. In this case, we can use the principle of conservation of momentum to solve for the velocity of the larger cart after the collision.

Before the collision, the small cart has a mass of 0.3 kg and a velocity of 1.8 m/s. The larger cart has a mass of 1.0 kg and is at rest. After the collision, the small cart recoils with a velocity of 0.81 m/s.

Using the conservation of momentum equation:

(mass of small cart * initial velocity of small cart) + (mass of large cart * initial velocity of large cart) = (mass of small cart * final velocity of small cart) + (mass of large cart * final velocity of large cart)

(0.3 kg * 1.8 m/s) + (1.0 kg * 0 m/s) = (0.3 kg * 0.81 m/s) + (1.0 kg * final velocity of large cart)

After solving this equation, we find that the velocity of the larger cart after the collision is 0.18 m/s. Therefore, the correct answer is option a) 0.18 m/s.