To practice problem-solving strategy 7.1 problems using mechanical energy i. 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. you can ignore air resistance and the mass of the vine.

Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. the hot water is to be used when needed. the drawback is that energy is wasted because the tank loses heat when it is not in use, and you can run out of hot water if you use too much. some utility companies are encouraging the use of on-demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. no water tank is involved, so no heat is wasted. a typical household shower flow rate is 2.50 gal/min (9.46 l/min ) with the tap water being heated from 51.0 ˚f (10.6 ˚c) to 120 ˚f (48.9 ˚c) by the on-demand heater. what rate of heat input (either electrical of from gas) is required to operate such a unit, assuming that all the heat goes into the water?