Question

The terminal velocity of a person falling in air depends upon the weight and the area of the person facing the fluid. Find the terminal velocity (in meters per second and kilometers per hour) of an 80.0-kg skydiver falling in a headfirst position with a surface area of 0.140 m2.

Answer 1

v=115 m/s

or

v=414 km/h

Step-by-step explanation:

Given data

`A_(area)=0.140m^(2)\\ p_(air)=1.21 kg/m^(3)\\ m_(mass)=80kg`

To find

Terminal velocity (in meters per second and kilometers per hour)

Solution

At terminal speed the weight equal the drag force

`mg=1/2*C*p_(air)*v^(2)*A_(area)\\ v=\sqrt{(2*m*g)/(C**p_(air)*A_(area)) }\\ Where C=0.7\\v=\sqrt{(2*9.8*80)/(1.21*0.14*0.7) }\\ v=115m/s`

For speed in km/h(kilometers per hour)

To convert m/s to km/h you need to multiply the speed value by 3.6

`v=(115*3.6)km/h\\v=414km/h`