Question

A 8 kg ball is moving at a speed of 12 m/s. It collides with 2 balls simultaneously, each having a mass of 3 kg. What is the final velocity of EACH BALL? (Draw a picture to help you answer the question) 6 m/s 16 m/s 32 m/s 96 m/s

Answer 1

To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.

Let's assume that the initial velocity of the 8 kg ball is v1, and the initial velocity of the two 3 kg balls is v2.

Initial momentum = Final momentum

m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'

where m1 is the mass of the 8 kg ball, m2 is the mass of each 3 kg ball, v1 is the initial velocity of the 8 kg ball, v2 is the initial velocity of the 3 kg balls, v1' is the final velocity of the 8 kg ball, and v2' is the final velocity of the 3 kg balls.

In this case, m1 = 8 kg, m2 = 3 kg, v1 = 12 m/s.

Using the conservation of momentum equation, we can calculate the final velocity of the 8 kg ball (v1').

8 kg * 12 m/s + 3 kg * v2 = 8 kg * v1' + 3 kg * v2'

96 kg m/s + 3 kg * v2 = 8 kg * v1' + 3 kg * v2'

Simplifying the equation, we get:

96 kg m/s = 8 kg * v1'

Dividing both sides of the equation by 8 kg, we find:

v1' = 12 m/s

So, the final velocity of the 8 kg ball is 12 m/s.

Since the two 3 kg balls are initially at rest (v2 = 0), we have:

8 kg * 12 m/s + 3 kg * 0 = 8 kg * v1' + 3 kg * v2'

96 kg m/s = 8 kg * v1' + 0

8 kg * v1' = 96 kg m/s

Dividing both sides of the equation by 8 kg, we find:

v1' = 12 m/s

So, the final velocity of each 3 kg ball is 12 m/s.

Therefore, the final velocity of EACH BALL is 12 m/s.