Answer:
The gravitational potential energy is 784,550 J.
Explanation:
In our case, the worded problem is about gravitational potential energy (GPE).
For the formula, we will use
GPE = mgh
where
GPE is the gravitaional potential energy, unit is in Joules (J)
m is the mass of the object, unit is in kg
g is the acceleration due to gravity, 9.8 m/[tex]s^2[/tex]
h is the height or altitude of the object, unit is in meters
For the given information
GPE = 1870J at h = 2.20 m
GPE = ? at h = 923 m
Solving the problem
In this problem, the mass of the object is constant. So, we should find the mass of Larry so that we can solve his GPE when he is at 923 m high above the ground.
1. Using the formula for GPE, substitute the given information to solve for Larry's mass
GPE = mgh
1870 J = m (9.8 m/[tex]s^2[/tex])(2.20 m)
Divide both sides of the equation by (9.8 m/[tex]s^2[/tex])(2.20 m), we have:
[tex]\frac{1870J}{(9.8m/s^2)(2.20m)} =\frac{m(9.8 m/s^2)(2.20 m)}{(9.8 m/s^2)(2.20 m)}[/tex]
[tex]m=\frac{1870J}{(9.8 m/s^2)(2.20 m)}[/tex]
m = 86.73 kg
2. Now, we are ready to solve for the GPE of Larry with an altitude of 923 m
Using the same formula, substitute Larry's mass and his new altitude.
GPE = mgh
GPE = (86.73 kg)(9.8 m/[tex]s^2[/tex])(923 m)
GPE = 784,550 J
Therefore, Larry's gravitational potential energy at 923 m altitude is 784,550 J.
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