Answer: 104.026 m/s=374.49 km/h
Explanation:
When a body or object falls, basically two forces act on it:
1. The force of air friction, also called "drag force" [tex]D[/tex]:
[tex]D={C}_{d}\frac{\rho V^{2} }{2}A[/tex] (1)
Where:
[tex]C_ {d}=0.7[/tex] is the drag coefficient
[tex]\rho=1.21 kg/m^{3}[/tex] is the density of the fluid (air in this case)
[tex]V[/tex] is the velocity
[tex]A=0.17 m^{2}[/tex] is the transversal area of the object
So, this force is proportional to the transversal area of the falling element and to the square of the velocity.
2. Its weight due to the gravity force [tex]W[/tex]:
[tex]W=m.g[/tex] (2)
Where:
[tex]m=79.5 kg[/tex] is the mass of the object
[tex]g=9.8 m/s^{2}[/tex] is the acceleration due gravity
[tex]D=W[/tex] (3)
[tex]{C}_{d}\frac{\rho V^{2} }{2}A=m.g[/tex] (4)
[tex]V=\sqrt{\frac{2m.g}{\rho A{C}_{d}}}[/tex] (5) This is the terminal velocity
Substituting the known values in (5):
[tex]V=\sqrt{\frac{2(79.5 kg)(9.8 m/s^{2})}{(1.21 kg/m^{3})(0.17m^{2}){(0.7)}}[/tex] (6)
Then:
[tex]V=104.026 m/s[/tex] This is the final velocity in meters per second
Now, let's find the final velocity in kilometers per hour, knowing [tex]1 km=1000 m[/tex] and [tex]1 h=3600 s[/tex]:
[tex]V=104.026 \frac{m}{s} (\frac{1 km}{1000 m})(\frac{3600 s}{1 h})=374.49 km/h[/tex] This is the final velocity in kilometers per hour.
