So, what do you do when your model doesn't give you the results you expect? Run the model for a wider range of wind speeds. Here is a plot of the displacement as a function of wind speed up to 10 m/s wind (about 20 mph).

Why is this so linear? Essentially, the jumper has enough falling time to reach the horizontal speed almost equal to the wind speed. So, faster wind means greater horizontal falling speed. Of course, with a high speed the jumper can be off from the starting position by as much as 2km - but that is the extreme case.

How about a comparison? What if the jumper started at rest with respect to the rotating Earth? How much would the displacement be in that case? I don't even really need to model this one. Let me just take the falling time of about 300 seconds. How far horizontally would the Earth's ground move in this time? Of course this depends on the location of the jump. The official launch site is in Roswell, New Mexico. This is located 33.39° above the equator. Here is a diagram of its position on the Earth.

The rotational speed of the Earth is *about** once a day, this is 7.27 x 10^{-5} radians per day. (* don't forget the difference between sidereal and solar days - but the difference hardly matters here). To find the velocity of a point on the ground, I need to radius of the circle that point is moving in. From the diagram above, this will be:

Using the radius of the Earth (6.38 x 10^{6} m) and the latitude of Roswell, this gives an distance of 5.33 x 10^{6} meters. The velocity of the ground will then be:

Putting in values from above, I get a speed of 387 m/s. So, in 300 seconds the ground will move 116 km (72 miles). Crazy, right? but remember in a whole day, this point on the ground has to go ALL THE WAY around the Earth. At this latitude, this is a path length of 20,000 miles.

So, why won't the jumper (Felix) be displaced by 70 miles when he jumps? Simple. He starts his jump with a velocity of about zero m/s relative to the ground. Yes, since he is higher up, he will have a different linear velocity than the ground - but the difference is super small.

## Homework

What about the centrifugal and Coriolis forces? How much will these change the motion of a jumper from 120,000 feet?