# Homework Help: Word problem help

1. Jan 4, 2005

### ccf788

Jane, looking for Tarzan, is running at top speed (5.6 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward?

I know the answer is 1.6 m, but I don't understand how to get it.

In class, we have been using the equation: 1/2mv^2 + mgy = 1/2mv^2 + mgy (where the first pt. of the equation is v1 and y1, and the second pt. v2 and y2. I don't understand how you would solve it if 5.6 m/s is the only number you have. I think it has something to do with gravity, but I'm not sure what.

Please show me how to solve it. Thanks!

2. Jan 4, 2005

### cepheid

Staff Emeritus
Define potential energy to be zero at the point just below the vine when it is vertical...ie this is the reference point. So initially, Jane's KE can be calculated from her velocity as she grabs the vine, and her PE is zero. When she swings upward, her KE is converted to gravitational potential energy. At the top of her swing, all of it has been converted, her velocity is zero, so she can go no further. Assuming only conservative forces, we can use conservation of mechanical energy as you suggested, except that based on what I said, it is in this form:

1/2mv2 + 0 = 0 + mgy

Solve for y