Question

Two ropes are attached to the bumper of a car. Rope A is pulled with a force of 60 pounds at an angle of 30° to the horizontal ground, and rope B is pulled with a force of 80 pounds at an angle of 15° to the horizontal ground. The same effect can be produced by a single rope pulling with what force and at what angle to the ground?

Answer 1

The forces caused by these two ropes could be equally produced by a single rope pulling at 138.82 pounds at an angle of 21.42 degrees to the horizontal ground. This can be found by considering each rope as the hypotenuse of a triangle. One leg of these triangles is the ground, and the other is perpendicular to the ground. Using Sine and Cosine you can find the components of the force in the horizontal and vertical directions. These are then added to find the resultant force components. The pythagorean theorem can then be used to find the net force of 138.82 pounds, and inverse tangent can be used to find the resultant angle of 21.42 degrees. *These calculations were done to two significant digits. If more precision is desired you can repeat these calculations to the desired number of significant digits.