Question

If the hiker starts climbing at an elevation of 350 ft, what will their change in gravitational potential energy be, in joules, once they reach the top

Answer 1

Answer:

352,088.37888Joules

Explanation:

Complete question;

A hiker of mass 53 kg is going to climb a mountain with elevation 2,574 ft.

A) If the hiker starts climbing at an elevation of 350 ft., what will their change in gravitational potential energy be, in joules, once they reach the top? (Assume the zero of gravitational potential is at sea level)

Chane in potential energy is expressed as;

ΔGPH = mgΔH

m is the mass of the hiker

g is the acceleration due to gravity;

ΔH is the change in height

Given

m = 53kg

g = 9.8m/s²

ΔH = 2574-350 = 2224ft

since 1ft = 0.3048m

2224ft = (2224*0.3048)m = 677.8752m

Required

Gravitational potential energy

Substitute the values into the formula;

ΔGPH = mgΔH

ΔGPH = 53(9.8)(677.8752)

ΔGPH = 352,088.37888Joules

Hence the gravitational potential energy is 352,088.37888Joules

Answer 2

The change in gravitational potential energy be, once the hiker reach the top of the mountain is 352088 joules or 352.1 kJ.

What is gravitational potential energy?

Gravitational potential energy is the energy which a body posses because of its position.

The gravitational potential energy of a body is given as,

$U=mgh$

Here, (m) is the mass of the body, (g) is the gravitational force and (h) is the height of the body.

The mass of the hiker is 53 kg and the height of the climb is 2574 ft.

Now, the hiker starts climbing at an elevation of 350 ft. Thus, the net height of the hiker has to climb is,

$h=2574-350\\h=2224\rm\; ft$

Convert this into the meter by multiplying 03048 as,

$h=2224\times0.3048\\h=677.8752\rm\; m$

It is known that the value of g is 9.8 m/s². Plug in all the values as,

$U=53\times9.8\times677.8752\\U=352088J\\U=352.1 \;\rm kJ$

Thus, the change in gravitational potential energy be, once the hiker reach the top of the mountain is 352088 joules or 352.1 kJ.

Learn more about the gravitational potential energy here;

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