If a car of mass 1000kg travels up a slope inclined at 5 degrees at a speed of 20 meters per second calculate the power output of the car's engine (assuming a resistive force due to friction of 500N)

To find power we are going to need the equation:

P = F v 

Where P is power, F is force and v is velocity

Since the car is travelling at a constant speed up the slope, we know that velocity, v is positive 20 meters per second.

The next step is to determine the force.

In mechanics it is important not to overlook any forces (or components of forces) that might be acting. 

We must consider the force due to gravity and the resistive force due to friction as counterpoints to the driving force of the engine.

First, considering the force due to gravity:

 We must resolve parallel to the plane of the slope, in order to determine the force against which the engine works. This is done by taking the product of mass and the acceleration due to gravity, mg, to find the weight: 10009.81 = 9810 Newtons and then resolving parallel with sin(5), giving 10009.81*sin(5) = 855 (rounded).

Knowing the force due to friction as 500 Newtons, we sum to get F = 855 + 500 = 1355

With our original equation P = F v we have:

P = 1355 * 20 = 27.1 kW