Question
A 65 kg person is standing on a roof that is 4.5 m high. What is the gravitational potential energy person? a. What is the person's potential energy when he is halfway to the ground? __ b. What is the person's kinetic energy when he is halfway to the ground? __ c. What is the kinetic energy of the person just as he hits the ground? __
Answer
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Faye
Elite · Tutor for 8 years
Answer
a. The person's potential energy when he is halfway to the ground is half of the initial 2860 joules, which is 1430 joules.b. The person's kinetic energy when he is halfway to the ground is calculated as
joules.c. The kinetic energy of the person just as he hits the ground is equivalent to the initial potential energy, which was 2860 joules.
Explanation
## Step1 ### The formula for gravitational potential energy is: ###
where
is mass,
is the acceleration due to gravity (which we'll take as 9.8 m/s²), and
is the height.## Step2 When the person is halfway to the ground, his gravitational potential energy is half of the initial. This means we substitute the values into the formula:###
## Step3 For kinetic energy when the person is halfway to the ground, the potential energy has been transformed into kinetic energy. According to the law of conservation of energy, the total energy in a system remains constant. Therefore, the kinetic energy can be calculated by subtracting the potential energy from the total energy:###
## Step4 When the person falls to the ground, all the potential energy is converted into kinetic energy. Therefore, the kinetic energy at this point is equal to the initial potential energy.