a 71.6 kg weight - watcher wishes to climb a ...
a 71.6 kg weight - watcher wishes to climb a mountain to work off the equivalent of a large piece of chocolate cake rated at 648 (food) calories. how high must the person climb? the acceleration due to gravity is 9.8 m/s² and 1 food calorie is 10³ calories. answer in units of km.
Answer
# Explanation:
## Step1: Convert food - calorie to joules
1 food - calorie = 4186 J, so 10^3 food - calories = 10^3×4186 J = 4.186×10^6 J.
## Step2: Use the work - energy theorem for gravitational potential energy
The work done in climbing is equal to the change in gravitational potential energy, \(W = mgh\). We know \(m = 71.6\ kg\), \(g=9.8\ m/s^{2}\), and \(W = 4.186×10^{6}\ J\). Rearranging the formula \(h=\frac{W}{mg}\).
## Step3: Substitute the values
\[h=\frac{4.186\times 10^{6}\ J}{71.6\ kg\times9.8\ m/s^{2}}\]
\[h=\frac{4.186\times 10^{6}}{71.6\times9.8}\ m\]
\[h=\frac{4.186\times 10^{6}}{701.68}\ m\approx5965.7\ m\]
\[h = 5.97\ km\] (rounded to two decimal places)
# Answer:
5.97 km