Using Octave or MATLAB; Given, the mass of John is 100 kg, the mass of the chute

Question

Using Octave or MATLAB;

Given, the mass of John is 100 kg, the mass of the chute alone is 5kg. Assuming the body area of John Kruger to be 1 m2 and the area of the closed chute to be 0.5 m2. Now assume that the airplane is at 5000 m. The parachute has an area of 0.5 m^2 and leaves the airplane 45 seconds before John. Plot both the parachute (red) falling and John falling head down with an area of 0.3 m^2 (blue) on the same plot. Plot the position graph above the velocity graph.

Assume that John leaves the airplane in the head down (area is 0.3 m) position 45 seconds after the parachute. At what time does John catch the parachute? Time is measured from when the parachute left the airplane.

Assume that John leaves the airplane in the head down (area is 0.3 m) position 45 seconds after the parachute. At what height does John catch the parachute? Time is measured from when the parachute left the airplane.

Explanation / Answer

Newton's universal law of gravity says that the force is proportional to the gravitational mass of the object, F=k1mg where k1 is a constant. Newton's second law of motion says that the acceleration is inversely proportional to the inertial mass and directly proportional to the applied force, F=k2mia; in SI units, k2=1. Therefore, a=k1mg/mi. (This is Einstein's statement "…the acceleration of a falling body increases in proportion to its gravitational mass and decreases in proportion to its inertial mass.") Now, since it is an experimental fact that a is the same regardless of the mass, mg/mi is a constant. If we choose to measure both mg and mi in kilograms, and since k1 expresses the strength of the gravitational field, mg/mi=1. (For the field near the earth's surface, k1=MearthG/Rearth where G is the universal gravitational constant, Mearthis the gravitational mass of the earth, and Rearth is the radius of the earth.)

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