What are the velocities of a golf ball and a billiard ball after an elastic collision in one dimension?

Question

Aida · Answer

In an elastic collision, both momentum and kinetic energy are conserved. First, we need to calculate the initial momentum of both balls:

Initial Momentum of Golf Ball:
P(golf ball) = m(golf ball) x v(golf ball) = 0.750 kg x 22 m/s = 16.5 kg*m/s to the right

Initial Momentum of Billiard Ball:
P(billiard ball) = m(billiard ball) x v(billiard ball) = 0.050 kg x (-15.0 m/s) = -0.75 kg*m/s to the left

Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision:
P(total) before = P(total) after
16.5 kg*m/s - 0.75 kg*m/s = m(total) x v(total) after
m(total) = 0.750 kg + 0.050 kg = 0.8 kg
v(total) after = (16.5 kg*m/s - 0.75 kg*m/s) / 0.8 kg = 20.4375 m/s to the right

Now, we need to calculate the individual velocities of each ball after the collision using the conservation of kinetic energy equation.

What Happens After an Elastic Collision Between a Golf Ball and a Billiard Ball?

Calculating Velocities After the Elastic Collision:

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