Your car is in a ditch. It requires 4500 N of force to get out of the ditch but you can only push with 750 N.

What is the angle the rope needs to make, relative to straight across the road for you to be able to get the car out of the ditch?

What is actually pulling the car out?

To calculate the angle at which the rope needs to be positioned relative to straight across the road, we can use trigonometry. Let's assume that the rope forms a right triangle with the horizontal road. The force you can exert, 750 N, acts as the hypotenuse of this triangle. The force required to get the car out of the ditch, 4500 N, acts as the opposite side of the triangle.

Using the trigonometric function sine (sin) in this scenario, we can set up the equation:

sin(angle) = opposite / hypotenuse

Rearranging the equation to isolate the angle, we get:

angle = arcsin(opposite / hypotenuse)

Plugging in the values, the equation becomes:

angle = arcsin(4500 / 750)

Calculating the value of this expression gives us:

angle ≈ 79.3°

Therefore, the angle the rope needs to make, relative to straight across the road, is approximately 79.3°.

Now, let's address what is actually pulling the car out of the ditch. In this scenario, the rope is essential to transferring the force you exert to the car. When you push with a force of 750 N, the rope transmits this force to the car, allowing it to move. This is possible due to the tension force in the rope. The rope pulls the car out by exerting a force on it in the opposite direction of the ditch. The tension in the rope counters the frictional force between the car and the ditch, ultimately allowing the car to move and exit the ditch.