How Much Power Does a Car Need to Climb a Hill at 100 km/h?

[frosti]

Homework Statement

The mass of a car is 1500 kg. The shape of the body is such that its aerodynamic drag coefficient is D = 0.380 and frontal area is 2.50 m2. Assuming that the drag force is proportional to v^2 and ignoring other sources of friction, calculate the power required to maintain a speed of 100 km/h as the car climbs a long hill sloping at 3.50° the answer is in horsepower

Homework Equations

R = .5DpAv^2
P = Fv
1hp = 746W

The Attempt at a Solution

Total force the engine needs to overcome is the gravitational force at an angle and air resistance.
To find force, F = mgsin(theta) + .5 DpAv^2. Plugs everything in, F = (1500)(9.8)sin(3.5) + .5(.38)(1.29)(2.5)(27.78^2) = 1370.3N
To find power, P = 1370.3(27.78) = 38067W, 38067W = 51 hp.

I don't think my answer is correct. Can anyone offer any insight as to why? Thank you in advance.

 

[PhanthomJay]

Looks correct to me. You probably were expecting a bit more horse required?

 

[frosti]

I entered my answer into the online homework thing and it told me I was 10% within the correct answer. I just can't figure out what's wrong with what I did. Man...

 

[PhanthomJay]

Did you copy down the correct information given in the problem?