Problem 1

Problem 2

Problem 3

1) A 50.0 kg parachutist jumps from an airplane and falls against a quadratic drag force ( **F**_{drag} = - C v^{2} **v**/v) , with C = 0.200 kg/m with parachute closed and C = 20.0 kg/m with parachute open. The jump starts at 1000 m and the parachutist is in free fall for the first 10 seconds. Notice that at t = 10s there will be a sudden change of acceleration so you might need to used a shorter time step dt in your simulation.

Calculate and display the trajectory (you may represent the man as as a ball, and the parachute as a second ball on top), and print the terminal speeds before and after the parachute opens, the altitude at which the parachute opens, and the total time to reach the ground; also compare this time with the no drag fall time and print the ratio (with drag time/no drag time).

2) A 0.142 kg baseball has a terminal speed v_{t} in air of 95 mph (this value is measured by dropping the ball from very high) . The drag force acting on it is quadratic (**F**_{drag} = - C v^{2} **v**/v). You can calculate C from the information provided (m g = C v_{t}^{2}). The baseball leaves the bath with a speed of 100 m/s at an elevation angle of 35° from a height of 1 m.

Calculate and display trajectory, and print the flight time, maximum height, and landing point for both cases (with and without drag).

Find and print the elevation angle that would give maximum landing distance for both cases.

3) A 3.00 g leaf is dropped from a height of 2.00 m above ground. Assume the drag force is linear:** F**_{drag}=-b v **v**/v, where b = 0. 030 kg/s.

Calculate and display the trajectory (you may represent the leaf as a small ball), and print the terminal speed and time to reach the ground; also compare this time with the no drag fall time and print the ratio (with drag time/no drag time). Display the trajectory of the leaf without drag next to the one with drag for comparison purposes.

The project is due October 30 at 5 PM. You have to submit a working VPython program listing that does __all__ what the problem chosen asks for. For a student without programming experience I estimate it requires about 6 hours of work to complete (including learning how to do things in VPython). It will not graded in a sliding scale, just Complete vs Incomplete (= + 1/4 Letter Grade vs 0).