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Chapter 6: Problem 20

Sean climbs a tower that is \(82.3 \mathrm{m}\) high to make a jump with a parachute. The mass of Sean plus the parachute is \(68.0 \mathrm{kg} .\) If \(U=0\) at ground level, what is the potential energy of Sean and the parachute at the top of the tower?

Short Answer

Expert verified
Answer: The gravitational potential energy of Sean and the parachute at the top of the tower is approximately 55431.164 Joules (J).

Step by step solution

01

Write the formula for potential energy

To find the potential energy of Sean and the parachute at the top of the tower, we will use the formula for gravitational potential energy: \(PE = mgh\).
02

Identify the values given by the exercise

The height of the tower, \(h\), is 82.3 meters (m), and the mass of Sean plus the parachute, \(m\), is 68.0 kilograms (kg). The gravitational acceleration, \(g\), is approximately 9.81 meters per second squared (\(m/s^2\)).
03

Substitute the given values into the formula and solve

We can now substitute the given values into the potential energy formula: \(PE = mgh = (68.0\,\mathrm{kg})(9.81\,\mathrm{m/s^2})(82.3\,\mathrm{m})\) Now, we can calculate the potential energy: \(PE = (68.0)(9.81)(82.3) = 55431.164\,\mathrm{J}\) So, the potential energy of Sean and the parachute at the top of the tower is approximately 55431.164 Joules (J).

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