A hiker $($weight $75$kg$)$ is trying to gauge their nutritional needs for an upcoming hike. They are planning to climb a mountain, and their typical pre$-$hike breakfast provides the equivalent of $500$ food Calories $($kilocalories$).$ To simplify, let$’$s assume that they$’$re climbing straight up$,$ and that the mechanical efficiency of hiking as an activity is around $10\%.$ Using this approximation, how high would they need to climb in order for their body to use up the energy provided by their breakfast

$($at which point they should start thinking about a snack$)?$ To answer this question, think about how much of this energy will appear as external work, vs how much will appear as heat.