Suppose a vehicle travels 150 km at a speed of 30.0 m/s, and uses 3.0 gal of gasoline. only 30% of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. if the energy content of the fuel is 1.2 x 108 j/gal. what is the magnitude of the force exerted to keep the car moving at constant speed?

Only 30% of gasoline is used for useful work in that engine

Now it is given that 3 Gal gasoline is used in the car

So the actual gasoline used by engine will be

energy content of gasoline will be

Energy consumed by the engine will be given by

now let say engine applied F force against the air drag to move the car

So work done by the engine = energy consumed by it

so engine must have to apply 720 N force

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west