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:

power out to power in less than 100%

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s