Asky diver with a mass of 70kg jumps from an aircraft. the aerodynamic drag force acting on the sky diver is known to be fd=kv^2, where k=0.25n*s^2/m^2. determine the maximum speed of free fall for the sky diver and the speed reached after 100m of fall. plot the speed of the sky diver as a function of time and as a function of distance fallen

Explanation:

the maximum speed is reached when the drag force and the weight are at equilibrium, therefore:

To calculate the velocity after 100 meters, we can no longer assume equilibrium, therefore:

(1)

consider the next equation of motion:

If assuming initial velocity=0:

(2)

joining (1) and (2):

(3)

To plot velocity as a function of distance, just plot equation (3).

To plot velocity as a function of time, you have to consider the next equation of motion:

as stated before, the initial velocity is 0:

(4)

joining (1) and (4) and reducing you will get:

solving for v:

Plots:

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