a 71.6 kg weight - watcher wishes to climb a mountain to work off the equivalent of a large piece of…

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.

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