Mechanical Energy - Two Questions

[JeremyM]

The questions read...

1.) An Olympic runner leaps over a hurdle. If the runner's initial vertical speed is 2.2 m/s, how much will the runner's center of mass be raised during the jump?

2.) A pendulum bob is released from some initial height such that the speed of the bob at the bottom of the swing is 1.9 m/s. What is the initial height of the bob?


What are the formulas I would use? I only want the formulas for now because I would like to try and solve it myself. Thanks!

 

[Diane_]

Well, I won't give you the formulas, but I'll give you a hint or two.

On the first one, the problem is the same as if you asked "what height would an object reach if it's initial speed were 2.2 m/s vertically upward?". The fact that they're asking about the runner's COM makes no difference.

For number 2, think about it from energy considerations - at the bottom of its arc, the pendulum bob has a certain amount of kinetic energy. Where did that energy come from?