10. Conservation of Energy

A slingshot will shoot a $10$-g pebble $22.0$ m straight up. With the same potential energy stored in the rubber band, how high can the slingshot shoot a $25$-g pebble? What physical effects did you ignore in solving this problem?

Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length $20$ m that makes an angle of $45°$ with the vertical, steps off his tree limb, and swings down and then up to Jane's open arms. When he arrives, his vine makes an angle of $30°$ with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Tarzan's speed just before he reaches Jane. Ignore air resistance and the mass of the vine.

The maximum height a typical human can jump from a crouched start is about $60$ cm. By how much does the gravitational potential energy increase for a $72$-kg person in such a jump? Where does this energy come from?

A slingshot will shoot a $10$-g pebble $22.0$ m straight up. How much potential energy is stored in the slingshot's rubber band?