Question

A hiker of mass 76kg is going to climb to the top of Mount Tam, which has an elevation of 2574ft

if the hiker starts climbing at an elevation of 595ft what will their change in gravitational potential energy be in joules, once they reach the top? assume the zero of gravitational potential energy at sea level

Answer 1

The change in gravitational potential energy for a 76kg hiker climbing to the top of Mount Tam, with an elevation change from 595ft to 2574ft, is 448,932.4 joules.

Step-by-step explanation:

To calculate the change in gravitational potential energy for the hiker, we use the formula ΔU = mgh, where ΔU is the change in potential energy, m is the mass of the hiker, g is the acceleration due to gravity, and h is the change in height. First, we convert the heights from feet to meters (since the standard unit of gravity, g, is in meters per second squared):

• Mount Tam's elevation: 2574 ft = 784.35 m (using the conversion 1 ft = 0.3048 m)
• Hiker's starting elevation: 595 ft = 181.36 m

Now, calculate the change in height (h): h = 784.35 m - 181.36 m = 603 m.

The mass of the hiker (m) is 76 kg and the standard acceleration due to gravity (g) is 9.8 m/s2. Substituting these values into the formula:

ΔU = (76 kg) × (9.8 m/s2) × (603 m)

ΔU = 448,932.4 J

Thus, once the hiker reaches the summit, their change in gravitational potential energy will be 448,932.4 joules with respect to sea level.