Answer:
a force of 1250lb is exerted
Step-by-step explanation:
since the force of the wind varies jointly as the area of the surface and the square of the velocity,
let f = force
a = area
velocity =v
from the above statement, we find out that
[tex]f \alpha a*v^2[/tex]----1
that is [tex]f= k* a* v^2[/tex] -----2
where k is a coefficent of proportionality
since velocity of wind in mph,v =50
and force in lb = 20
and surface area =[tex]1/5 th ft^2[/tex]
from eqn 2
we have that
[tex]20 =k*\frac{1}{5}* 50^2[/tex]
making k subject of the formula
we have that
[tex]k =\frac{20}{\frac{1}{5} *50^2 } =\frac{1}{25} (lb.mph^-1.ft^-2)[/tex]
that means that [tex]f =\frac{1}{25} *a *v^2[/tex] ---3
however, when velocity = 125mph
surface area =[tex]2ft^2[/tex]
putting values in eqn 3 we have
[tex]f= \frac{1}{25}*2*125^2 = 1250 lb[/tex]
hence a force of 1250lb is exerted
