A person jumped out of a plane and began falling to the surface of the Earth at a rate of 9.8 m/s².The person and their equipment have a total mass of 95 kg.After 30 seconds they have reached a speed of 50 m/s with a kinetic energy store of energy of 118 750 J.During this fall the person has had a change in gravitational energy of 2.3 MJ.Calculate the energy transferred to the surroundings.
Question
A person jumped out of a plane and began falling to the surface of the Earth at a rate of 9.8 m/s².The person and their equipment have a total mass of 95 kg.After 30 seconds they have reached a speed of 50 m/s with a kinetic energy store of energy of 118 750 J.During this fall the person has had a change in gravitational energy of 2.3 MJ.Calculate the energy transferred to the surroundings.
Solution
To calculate the energy transferred to the surroundings, we first need to understand the energy changes that have occurred.
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The person has gained kinetic energy, which we know is 118,750 J.
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The person has also lost gravitational potential energy, which is 2.3 MJ or 2,300,000 J.
The total energy change is the sum of these two, which is 2,300,000 J + 118,750 J = 2,418,750 J.
However, we know that the person has only reached a speed that gives them 118,750 J of kinetic energy. This means that the rest of the energy must have been transferred to the surroundings.
So, the energy transferred to the surroundings is the total energy change minus the kinetic energy gained.
That is, 2,418,750 J - 118,750 J = 2,300,000 J.
So, the energy transferred to the surroundings is 2.3 MJ.
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