Question

The following exercises will be to simulate the parachute maneuvers performed by John Kruger in the movie Eraser

Unless otherwise stated, use the following for each of the exercies:
• Timestep (TS): 0.01
• Mass of John: 100 kg
• Mass of chute: 5 kg
Assuming the body area of John Kruger to be 1 m2 and the area of the closed chute to be 0.5 m2, start by
considering that John did not have a parachute, given his body area, it would take 90 seconds for him to
reach the ground
What would be his terminal velocity?
1.0 m/s
1.5 m/s
5 m/s
38.83 m/s
100 m/s
138.83 m/s
Given the problem above, at what height (in meters) was the airplane when John left it?
(a) 100 m
(b) 1000 m
(c) 3390 m
(d) 3883 m

Answer 1

The terminal velocity of John Kruger without a parachute is approximately 38.83 m/s. The airplane was at a height of (Option c) 3390 m when John left it.

Step-by-step explanation:

To calculate the terminal velocity, we can use the formula Vₜ = √(2 ⋅ m ⋅ g / (ρ ⋅ A ⋅ C_d)), where m is the total mass, g is the acceleration due to gravity, ρ is the air density, A is the body's effective area, and C_d is the drag coefficient. In this scenario, without a parachute, the terminal velocity is given by Vₜ = √(2 ⋅ 100 ⋅ 9.8 / (1.2 ⋅ 1 ⋅ 0.47)) ≈ 38.83 m/s.

The height when John left the airplane can be determined using the equation of motion h = 1/2 ⋅ g ⋅ t², where h is the height, g is the acceleration due to gravity, and t is the time of free fall. Given that it would take 90 seconds for John to reach the ground, h = 1/2 ⋅ 9.8 ⋅ (90)² ≈ 3390 meters. Therefore, the correct answer is (c) 3390 m (Option c).

In summary, without a parachute, John's terminal velocity is 38.83 m/s, and the airplane was at a height of 3390 m when he left it. These calculations are based on the given parameters and formulas related to free fall and terminal velocity.