TTU Dynamics - Energy Analysis in American Units

[Green Lantern]

I am having a problem with dynamics this semester. Our professor gives us "FE-like" questions, which are actually more complicated than FE questions. I can get to where I need to apply the kinetic energy equation but my units look really large and I don't know what to do with W' or how I can get opposing head wind velocity from that.

Homework Statement

An automobile, weighing 1500 lbf is being driven at 50 mph utilizing 75 hp when
it it struck by head wind that drops its speed by 20%. How fast was the wind?
Ignore all friction but air drag.

Homework Equations

F = ma
E = (T+V)
T = (1/2)mv²

The Attempt at a Solution

F = 1500 lbf
v₁ = 50 mph
W' = 75 hp
ε = -20%

F = ma: 1500 = m(32.17)
m = 46.63 sl

v₂ = v₁(1 + ε): v₂ = 50(1 - 0.2)
v₂ = 40 mph

1 = 1.46 fps
∴v₁ = 73 fps and v₂ = 58.4 fpsT₁ = (1/2)mv₁²: T₁ = (1/2)(46.63)(73²)
T₁ =

T₂ = (1/2)mv₂²: T₂ = (1/2)(46.63)(58.4²)
T₂ =

The units here don't make sense, since I need to use lbf to get horsepower. Is there a way I can apply force to energy?

 

[Valkarie]

Since the power is given, you can use the equation W' = Fv to solve for the wind velocity. W' = Fv: 75 hp = (1500 lbf)(v)v = 0.05 mphTherefore, the opposing head wind velocity is 0.05 mph.