Question

A runner is training for a race by running up a hill. The 85kg racer runs a 40m path to reach a height of 5m above where they started (see diagram below). Their legs put in a consistent force of 320N for the entire distance a) How much potential energy did the runner gain? (2 marks) b) How much energy was put into the system (2 marks) c) If the run took 15 seconds, what is the power rating of the runner's legs? (2 marks) d) Assuming perfect efficiency, what is the runner's kinetic energy at the top of the hill? (2 marks) e) What is the run speed at the top of the hill? (2 marks) 5m high 40m long

Answer 1

a.

Potential energy gained,

b.

Energy Input,

c.

Power, $P = \frac{E}{t} = \frac{12800}{15} = 853.33 W$

d.

Kinetic energy at the top,

e.

Velocity at the top, $v =\sqrt{ \frac{2KE}{m}} = \sqrt{ \frac{2*8635}{85}}= 14.25 m/s$