Suppose that the terminal speed of a particular sky diver is 170 km/h in the spread-eagle position and 315 km/h in the nosedive position. Assuming that the diver's drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in the faster position (Aslower / Afaster).

To find the ratio of the effective cross-sectional area in the slower position to that in the faster position, we can use the equation for drag force:

Fd = (1/2) * C * A * ρ * V^2

Where:
- Fd is the drag force
- C is the drag coefficient
- A is the effective cross-sectional area
- ρ (rho) is the density of the fluid (in this case, air)
- V is the velocity of the object relative to the fluid

In this case, we have two different velocities: 170 km/h and 315 km/h. We need to find the ratio of the cross-sectional areas, so we can set up the following equation:

Fd_slower = (1/2) * C * Aslower * ρ * Vslower^2
Fd_faster = (1/2) * C * Afaster * ρ * Vfaster^2

Since the only variable that changes is the velocity, we can divide the two equations to eliminate the drag force and density:

Fd_slower / Fd_faster = (Aslower * Vslower^2) / (Afaster * Vfaster^2)

We are given that the terminal speed in the spread-eagle position is 170 km/h and in the nosedive position is 315 km/h. We can use these values to substitute into the equation:

(Aslower * (170 km/h)^2) / (Afaster * (315 km/h)^2) = ?
(After converting the velocities to m/s)

To calculate the ratio, we need to convert the velocities from km/h to m/s, which is done by multiplying by (1000 m/1 km) * (1 h/3600 s):

(Aslower * (170 m/s)^2) / (Afaster * (315 m/s)^2) = ?

Simplifying further:

(Aslower * 28900) / (Afaster * 99225) = ?

Therefore, the ratio of the effective cross-sectional area in the slower position to that in the faster position is 28900 / 99225.