Answer: 52 kg skydiver: 9.09 m/s and 522.55 s
95 kg skydiver: 12.3 m/s and 386.2 s
Explanation: <u>Drag</u> <u>Force</u> is an opposite force when an object is moving in a fluid.
For skydivers, when falling through the air, the forces acting on it are gravitational and drag forces. At a certain point, drag force equals gravitational force, which is constant on any part of the planet, producing a net force that is zero. Since there is no net force, there is no acceleration and, consequently, velocity is constant. When that happens, the person reached the <u>Terminal</u> <u>Velocity</u>.
Drag Force and Velocity are proportional to the squared speed. So, terminal velocity is given by:
![F_{G}=F_{D}](https://tex.z-dn.net/?f=F_%7BG%7D%3DF_%7BD%7D)
![mg=\frac{1}{2}C \rho Av_{T}^{2}](https://tex.z-dn.net/?f=mg%3D%5Cfrac%7B1%7D%7B2%7DC%20%5Crho%20Av_%7BT%7D%5E%7B2%7D)
![v_{T}=\sqrt{\frac{2mg}{\rho CA} }](https://tex.z-dn.net/?f=v_%7BT%7D%3D%5Csqrt%7B%5Cfrac%7B2mg%7D%7B%5Crho%20CA%7D%20%7D)
where
m is mass in kg
g is acceleration due to gravitational force in m/s²
ρ is density of the fluid in kg/m³
C is drag coefficient
A is area of the object in the fluid in m²
Calculating:
The 52kg skydiver has terminal velocity of:
![v_{T}=\sqrt{\frac{2(52)(9.8)}{(1.21)(0.7)(0.14)} }](https://tex.z-dn.net/?f=v_%7BT%7D%3D%5Csqrt%7B%5Cfrac%7B2%2852%29%289.8%29%7D%7B%281.21%29%280.7%29%280.14%29%7D%20%7D)
9.09
The 95kg skydiver's terminal velocity is
![v_{T}=\sqrt{\frac{2(95)(9.8)}{(1.21)(0.7)(0.14)} }](https://tex.z-dn.net/?f=v_%7BT%7D%3D%5Csqrt%7B%5Cfrac%7B2%2895%29%289.8%29%7D%7B%281.21%29%280.7%29%280.14%29%7D%20%7D)
12.3
The 52 kg and 95kg skydivers' terminal velocity are 9.09m/s and 12.3m/s, respectively.
The time each one will reach the floor will be:
52 kg at 9.09 m/s:
![t=\frac{4750}{9.09}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B4750%7D%7B9.09%7D)
t = 522.5
95 kg at 12.3 m/s:
![t=\frac{4750}{12.3}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B4750%7D%7B12.3%7D)
t = 386.2
The 52 kg and 95kg skydivers' time to reach the floor are 522.5 s and 386.2 s, respectively.