Question

A mountain climber climbing a steep slope drops her water bottle. The bottle slides 100 m down an icy hill, 10 m lower (vertically) than where the climber dropped the bottle. The mass of the bottle is 0.5 kg.



a) What is the total mechanical energy of the bottle at the top of the hill?







b) What is the velocity of the bottle at the bottom of the hill?

Answer 1

a)

$$E=mgh=(0.5)(9.8)(10)=49\ J$$

b)

$$v=\sqrt{2gh}=\sqrt{2(9.8)(10)}=14\frac{m}{s}$$