Diver free fall diagram

Free body diagram in response to this question: https://www.reddit.com/r/gifs/comments/5rmq87/cruise_ship_high_dive/dd8vnej/

We've got to make some assumptions. Let's use this picture as a reference:

- We assume the ship has no wind screen or surrounding structure to buffer the still air.
- We assume the ship is moving at 20 mph uniformly along the green axis.
- We assume the diver is at a height (Hd) above the center of the pool (black x).
- We assume the diver does not jump, but releases herself from the platform, immediately going into freefall straight down toward the center of the pool.
- We assume the diver is represented by a 50kg mass, 2m tall and 0.5m wide, for a surface area of 1m^2 that is completely perpendicular to the axis of the ship's motion.
- We assume the diver does not tumble or spin in any way.
- We assume uniform gravity along the diver's descent of g = 9.8 m/s
- We assume the air pressure and density are completely uniform for an infinite height above the ship and the ocean.


The ship moving at 20 mph is equivalent to a uniform relative wind speed (Vw) of 20mph in the exact opposite direction. This will generate a force (F) on our diver that will push her ever so slightly backwards along the green axis toward the edge of the pool, and she will end up hitting the edge 10m from the center of the pool, at the red x.

Also, let's go ahead and convert that 20mph relative wind speed to SI units: 8.94 m/s

To calculate our wind force, we'll use the first formula here: http://www.wikihow.com/Calculate-Wind-Load

F = A*P*Cd

Subbing in the surface area of our diver (1 m^2), P = 0.613*Vw^2 = 0.613(8.94 m/s)^2, and Cd = 1.4 (for a shorter flat plate? works for me)

F = (1 m^2) * (48.99 N/m^2) * (1.4) = 68.59 N

Let's use our wind force to get the acceleration on our diver (mass of 50kg) :

F = ma

(68.59 N) = (50 kg)*a

a = (68.59 N)/(50kg) = 1.37 m/s^2

Then we can use that to determine the time it takes our diver to move 10m horizontally in the air:

d = (1/2)at^2

(10 m) = (1/2)*(1.37 m/s^2)*t^2

t = SQRT((10 m)/((1/2)*(1.37 m/s^2))) = 14.60 s

Then, let's just use this freefall with air resistance calculator because we're lazy and almost done: http://keisan.casio.com/exec/system/1224830797

Mass = 50 kg

Free fall time = 14.60 s

Air resistance k = .24 kg/m

Free fall distance = 515.89 m

In our scenario, our diver would have to start just over a half a kilometer in the air for her to miss the pool.