Quite new to all this - simple question.
"A ball starting from rest rolls down a hill and reaches 10m/s at the bottom. If the same ball starts rolling down the hill from an initial velocity of 5m/s, will it's velocity at the bottom be: (A) Less than 15m/s; (B) Equal to 15m/s; (C) Greater than 15m/s."
The answer I have marked in the book this question comes from says (A). However, I am unable to reason to that conclusion from the way the question is stated. Here is my reasoning, please point out where it is wrong. If the same ball (the same mass) traveses the same distance down this same hill (the same change in height), the gravitational potential energy must be the same at the point on top of the hill, regardless of its initial velocity. Therefore, on rolling down the hill, by the time it reaches the bottom, this potential energy would have transferred to kinetic energy - indicating (B)?
Thanks for your time.