Find the Power to move a car on an incline

[BSElectrician]

Homework Statement

What power is needed to move a 3000lb car up an 8 degree incline with a constant speed of 50mi/h against a frictionless force of 80lb?

ans. 68hp

Homework Equations

P = Fv

1hp = 550 lb-ft/s

The Attempt at a Solution

1st i draw free body diagram
summation of force in the horizontal direction
Fx = 0 = 3000sin(8) + 80 - Fn
Fn = 497.52lb

Power = velocity x force
= (50mi/h)(1/3600s)(1ft/0.3048m)(1000m/1km)(1km/0.62137mi)
= 36,485.56 lb-ft/s
= (36,485.56 lb-ft/s)(1hp/(550lb-ft/s))
= 66.34 horsepower
where did i get wronged?

 

[Delphi51]

I get the same answer you have.

 

[LawrenceC]

I think your answer is correct. I get the same result either by figuring the forces and multiplying by velocity (as you did) or by using the 80 pound force times velocity added to the change in potential energy per second.