There is something wrong with the assumptions of this problem. Collisions of bowling balls with pins are highly elastic. The kinetic energy of rotation of the bowling ball also should be considered. It changes very little.
A pin hit head-on by a bowling ball will end up with a velocity a lot faster than that of the ball. If you don't believe it, go to a bowling alley.
They probably want you to assume conservation of momentum for the collision. This is OK, but the assumed velocity of the pin after collision is not.
6.9*6.4 = 6.9V' + 6.4*1.4
V2 (the final velocity of the ball) = 5.1 m/s
Use that velocity and what you already know to compute the KE loss they want to to compute. Warning: it will not be close to what would really happen.
Your teacher may be unaware of the importance of rotational KE, so assume it stays the same.
A 6.9 kg bowling ball travelling at 6.4 m/s strikes a stationary 1.4 kg bowling pin. After the collision, the pin flies forward at 6.4 m/s.
How much kinetic energy was lost in the collision?
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