Question

A 0.3 kg marble is traveling at 4 m/s. It collides with a .5 kg marble traveling 3 m/s. After the collision the .5 kg marble rolls away at 5 m/s. What is the final velocity of the 0.3 kg marble?

Answer 1

The final velocity of the 0.3 kg marble is 5 m/s after the collision with the 0.5 kg marble.

Step-by-step explanation:

In this collision, we can use the principle of conservation of momentum to find the final velocity of the 0.3 kg marble. The principle states that the total momentum before the collision is equal to the total momentum after the collision.

Before the collision, the momentum of the 0.3 kg marble is given by:

Momentum1 = mass1 × velocity1

= 0.3 kg × 4 m/s

= 1.2 kg·m/s

After the collision, the two marbles stick together and move as one. So, the total momentum after the collision is:

Momentum2 = (mass1 + mass2) × velocity2

= (0.3 kg + 0.5 kg) × 5 m/s

= 0.8 kg × 5 m/s

= 4 kg·m/s

Since the total momentum before the collision is equal to the total momentum after the collision, we can equate the two values:

1.2 kg·m/s = 4 kg·m/s

Now, we can solve for the final velocity of the 0.3 kg marble:

velocity2 = total momentum after the collision / total mass after the collision

= 4 kg·m/s / (0.3 kg + 0.5 kg)

= 4 kg·m/s / 0.8 kg

= 5 m/s

So, the final velocity of the 0.3 kg marble is 5 m/s.