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.Calculate the kinetic energy store of the person and their equipment at this moment.
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.Calculate the kinetic energy store of the person and their equipment at this moment.
Solution 1
To calculate the kinetic energy, we can use the formula:
Kinetic Energy = 0.5 * mass * velocity²
Given in the problem, the mass (m) is 95 kg and the velocity (v) is 50 m/s.
Substituting these values into the formula, we get:
Kinetic Energy = 0.5 * 95 kg * (50 m/s)²
First, square the velocity:
50 m/s * 50 m/s = 2500 (m²/s²)
Then multiply this by the mass and 0.5:
0.5 * 95 kg * 2500 m²/s² = 118750 Joules
So, the kinetic energy store of the person and their equipment at this moment is 118750 Joules.
Solution 2
To calculate the kinetic energy of the person and their equipment, we can use the formula for kinetic energy:
KE = 0.5 * m * v²
where:
- KE is the kinetic energy,
- m is the mass of the object (in this case, the person and their equipment), and
- v is the velocity of the object.
Given in the problem, m = 95 kg and v = 50 m/s. Substituting these values into the formula gives:
KE = 0.5 * 95 kg * (50 m/s)² KE = 0.5 * 95 kg * 2500 m²/s² KE = 118750 Joules
So, the kinetic energy store of the person and their equipment at this moment is 118750 Joules.
Solution 3
To calculate the kinetic energy, we can use the formula:
KE = 0.5 * m * v²
where: KE is the kinetic energy, m is the mass (in kg), and v is the velocity (in m/s).
Given in the problem, m = 95 kg and v = 50 m/s.
Substituting these values into the formula, we get:
KE = 0.5 * 95 kg * (50 m/s)² KE = 0.5 * 95 kg * 2500 m²/s² KE = 0.5 * 237500 kg*m²/s² KE = 118750 Joules
So, the kinetic energy store of the person and their equipment at this moment is 118750 Joules.
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