1. after being struck by a bowling ball, a 1.5 kg bowling pin moving to the right at +3.0 m/s collides with
another 1.5 kg bowling pin at rest. find the velocity of the second pin when:
a. the first pin moves to the right after the collision at +0.5 m/s.
b. the first pin stops moving when it hits the second pin.

a) Final velocity of second bowling pin is 2.5m/s.

b) Final velocity of second bowling pin is 3 m/s.

Explanation:

Let 'm' be the mass of both the bowling pin -

m = 1.5 kg

Initial velocity of first bowling pin -

In any type of collision between two bodies in horizontal plane , momentum is conserved along the line of impact.

a) Since , initial velocity of second bowling pin is 0 m/s -

Initial momentum ,

Final velocity of first bowling pin , [Considering initial direction of motion of the first bowling pin to be positive]

Let be the final velocity of the second bowling pin.

∴ Final momentum ,

.

Now ,

∴

∴ = 3 - 0.5 = 2.5 m/s

∴ Final velocity of second bowling pin is 2.5 m/s.

b) Since , initial velocity of second bowling pin is 0 m/s -

Initial momentum ,

Final velocity of first bowling pin , [given][Considering initial direction of motion of the first bowling pin to be positive]

Let be the final velocity of the second bowling pin.

∴ Final momentum ,

.

Now ,

∴

∴ = 3 - 0 = 3 m/s

∴ Final velocity of second bowling pin is 3 m/s.