Question

A cart of mass 2.0 kg is moving to the right along a smooth, horizontal track at 3.0 m/s. What is the final velocity of the system after the head-on collision with the 4.0 kg kart initially at rest?

a) 1.5 m/s
b) 2.0 m/s
c) 2.5 m/s
d) 3.0 m/s

Answer 1

The final velocity of the system after the head-on collision is 3.0 m/s.

Step-by-step explanation:

To calculate the final velocity of the system after the head-on collision, we need to apply the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Using the formula:

m1 * v1 + m2 * v2 = (m1 + m2) * vf

We can plug in the values given: m1 = 2.0 kg, v1 = 3.0 m/s, m2 = 4.0 kg, and vf is the final velocity we need to find.

Plugging in these values, we have:

2.0 kg * 3.0 m/s + 4.0 kg * 0 m/s = (2.0 kg + 4.0 kg) * vf

Simplifying the equation:

6.0 kg * 3.0 m/s = 6.0 kg * vf

18.0 kg * m/s = 6.0 kg * vf

Dividing both sides by 6.0 kg:

3.0 m/s = vf

Therefore, the final velocity of the system after the head-on collision is 3.0 m/s.