In one day, a 85 kg mountain climber ascends from the 1440 m level on a vertical cliff to the top at 2360 m . The next day, she descends from the top to the base of the cliff, which is at an elevation of 1310 m .

a) What is her gravitational potential energy on the first day? If you choose the reference level for zero potential energy at:
a. the top of the cliff.
b. 1440 m level.
c. 1310 m level.
b) What is her change in gravitational potential energy on the first day?
c) What is her change in gravitational potential energy on the second day?

m g (H - Ho) where mg = 85*9.81 = 834 N

first day
If Ho = 2360
U at start = 834 (1440-2360)
U at top = 834 (2360-2360) = 0
If Ho = 1440
U at start = 834 (1440-1440) = 0
U at top = 834 (2360 - 1440)
If Ho = 1310
U at start = 834 (1440 - 1310)
U at top = 834 (2360 - 1310)

b) U at top - U at start
834(2360 - 1440)

c) U at end - U at top
834 (1310 - 2360)

To calculate the gravitational potential energy, we can use the formula:

Gravitational Potential Energy = Mass * Gravity * Height

Given:
Mass (m) = 85 kg
Gravity (g) = 9.8 m/s^2 (acceleration due to gravity)

a) What is her gravitational potential energy on the first day?

a. If we choose the reference level for zero potential energy at the top of the cliff (2360 m):

Gravitational Potential Energy = Mass * Gravity * Height
Gravitational Potential Energy = 85 kg * 9.8 m/s^2 * (2360 m - 2360 m)
Gravitational Potential Energy = 0 Joules

b. If we choose the reference level for zero potential energy to be at the 1440 m level:

Gravitational Potential Energy = Mass * Gravity * Height
Gravitational Potential Energy = 85 kg * 9.8 m/s^2 * (2360 m - 1440 m)
Gravitational Potential Energy = 85 kg * 9.8 m/s^2 * 920 m
Gravitational Potential Energy ≈ 746,960 Joules

c. If we choose the reference level for zero potential energy to be at the 1310 m level:

Gravitational Potential Energy = Mass * Gravity * Height
Gravitational Potential Energy = 85 kg * 9.8 m/s^2 * (2360 m - 1310 m)
Gravitational Potential Energy = 85 kg * 9.8 m/s^2 * 1050 m
Gravitational Potential Energy ≈ 86,2050 Joules

b) What is her change in gravitational potential energy on the first day?

Change in Gravitational Potential Energy = Final Gravitational Potential Energy - Initial Gravitational Potential Energy

Using the reference level at 1440 m:
Change in Gravitational Potential Energy = 746,960 Joules - 0 Joules
Change in Gravitational Potential Energy = 746,960 Joules

Using the reference level at 1310 m:
Change in Gravitational Potential Energy = 862,050 Joules - 0 Joules
Change in Gravitational Potential Energy = 862,050 Joules

c) What is her change in gravitational potential energy on the second day?

Using the reference level at 1310 m:
Change in Gravitational Potential Energy = 0 Joules - 862,050 Joules
Change in Gravitational Potential Energy = -862,050 Joules (negative because she is descending)

To determine the answers, we need to calculate the gravitational potential energy at different reference levels, and then calculate the change in gravitational potential energy on each day.

First, let's calculate the gravitational potential energy using the formula:

E = m * g * h

where E is the gravitational potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.

Given:
Mass (m) = 85 kg
Top of cliff (h1) = 2360 m
1440 m level (h2) = 1440 m
Base of the cliff (h3) = 1310 m

Acceleration due to gravity (g) is approximately 9.8 m/s^2.

a) Gravitational potential energy at the top of the cliff (h1):
E1 = m * g * h1
= 85 kg * 9.8 m/s^2 * 2360 m

b) Gravitational potential energy at the 1440 m level (h2):
E2 = m * g * h2
= 85 kg * 9.8 m/s^2 * 1440 m

c) Gravitational potential energy at the base of the cliff (h3):
E3 = m * g * h3
= 85 kg * 9.8 m/s^2 * 1310 m

To calculate the change in gravitational potential energy, we subtract the initial potential energy from the final potential energy:

Change in gravitational potential energy on the first day:
∆E1 = E1 - E2, assuming the reference level is the top of the cliff

Change in gravitational potential energy on the second day:
∆E2 = E1 - E3, assuming the reference level is the top of the cliff

Now, let's substitute the values to calculate the answers.