# Can someone explain to me the process of answering this question? I understand how to find the net force if all forces are in one direction but not if the forces are in different directions like...

Can someone explain to me the process of answering this question? I understand how to find the net force if all forces are in one direction but not if the forces are in different directions like the question below:

"Hercules is pulling a monument with a force of 100 N [E 45 N]. Superman is pulling the same monument with a force of 100 N [E 45 S]. A pedestrian is pulling the same monument with a force of 10 N [W]. What is the net force on the monument?"

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### 1 Answer

On the image attached below, `vecF_H` is the force applied to the monument by Hercules, `vecF_s` is the force applied to the monument by Superman, and `vecF_p`

is the force applied to the monument by a pedestrian. As you mentioned, Hercules' and Superman's forces are not along the same line. To add vectors like that, you can use the parallelogram rule: notice the parallelogram build on the force vectors, by drawing the lines parallel to each force. Then, the diagonal in between the two vectors will be the vector sum of the two forces, `vecF_h + vecF_s` , also shown on the image.

In this particular case, both Hercules' and Superman's forces make the same angle with the horizontal, 45 degrees. This means that vertical components of these forces will cancel each other out, and the net force for Hercules and Superman, `vecF_h + vecF_s` , will be directed only along the horizontal line, towards East. The magnitude of the net Hercules and Superman force will be the sum of the horizontal component of each force:

`F_hcos(45) + F_scos(45) = 100*sqrt(2)/2 + 100*sqrt(2)/2 = 100sqrt(2)` .

To find the net force for all three forces in this problem, we also need to add the pedestrian's force. It is now easy to do because it is along horizontal line, just like the net Hercules and Superman force. However, it is directed towards West, in the opposite direction to the net Hercules and Superman force. So the net force for all three forces will be also horizontal, directed toward East, and its magnitude will be the difference of the magnitudes of `vecF_h + vecF_s` and `vecF_p`:

`100sqrt(2) - 10 = 131.42 N`

**The net force on the monument is 131.42 N [E].**