Answer
(a) The mountain should be 920 meters high.
(b) The mountain should be 184 meters high.
Work Step by Step
(a) We can find the energy in the food.
$E = (140~calories)(4186~J/cal)$
$E = 586040~J$
We can equate the energy in the food to the hiker's change in potential energy.
$mgh = 586040~J$
$h = \frac{586040~J}{(65~kg)(9.80~m/s^2)}$
$h = 920~m$
The mountain should be 920 meters high.
(b) Since only 20% of the food energy goes into mechanical energy, the height of the mountain should be $20\% \times (920~m)$, which is 184 meters.
The mountain should be 184 meters high.
