Question

Johnny and his sister Jane race up a hill. Johnny weighs twice as much as Jane and takes twice as long as Jane to reach the top. Compared to Jane

• A. Johnny did more work and delivered more power.
• B. Johnny did more work and delivered the same amount of power.
• C. Johnny did more work and delivered less power
• D. Johnny did less work and Johnny delivered less power.

Answer 1

Answer: (B)

Johnny did more work and delivered the same amount of power.

The work is done against gravity so it is equal to the change in potential energy. $W=E_p=mgh$
For a fixed height, work is proportional to weight lifted. Since Johnny weighs twice as much as Jane he works twice as hard to get up the hill.
Power is work done per unit time. For Johnny this is $W/\Delta t$. Jane did half the work in half the time, $\left(1/2W\right)/\left(1/2\Delta t\right)=W/\Delta t$ which is the same power delivered by Johnny.