A villain is knocked out of a low-flying aircraft by a heroic scientist-adventurer at an altitude of 370 m. After falling for 120 m the villain reaches terminal velocity. 7.16 seconds after reaching terminal velocity, the villain crash lands in a river full of piranha. If the mass of the villain is 89 kg, how much work was done on him by air resistance?
To find the amount of work done on the villain by air resistance, we need to calculate the change in potential energy and kinetic energy.
1. First, let's find the potential energy of the villain when he is knocked out of the aircraft at an altitude of 370 m.
- The formula for potential energy is: potential energy = mass * acceleration due to gravity * height.
- The mass of the villain is given as 89 kg.
- The acceleration due to gravity is approximately 9.8 m/s^2.
- The height is 370 m.
- Substituting these values into the formula, we get: potential energy = 89 kg * 9.8 m/s^2 * 370 m.
2. Next, let's find the kinetic energy of the villain when he reaches terminal velocity.
- At terminal velocity, the villain stops accelerating and the net force on him becomes zero.
- The formula for kinetic energy is: kinetic energy = 0.5 * mass * velocity^2.
- Since terminal velocity means constant velocity, the kinetic energy remains constant.
- We do not have the value for the velocity, but we know that 7.16 seconds after reaching terminal velocity, the villain crash lands in a river.
- Assuming the velocity remains constant during this time, we can calculate the velocity using the distance fallen after reaching terminal velocity (120 m) divided by the time (7.16 seconds).
- Substituting the velocity value into the formula, we get: kinetic energy = 0.5 * 89 kg * velocity^2.
3. The work done by air resistance is equal to the change in potential energy minus the change in kinetic energy.
- We can calculate the change in potential energy by subtracting the potential energy at the starting point from the potential energy at the ending point.
- We can calculate the change in kinetic energy by subtracting the kinetic energy at the starting point from the kinetic energy at the ending point.
- The work done by air resistance is equal to the change in potential energy minus the change in kinetic energy.
By following these steps and calculating the values using the given information, you can determine the amount of work done on the villain by air resistance.