# The wind exerts a force of 452 N north on a sailboat, while the water exerts a force of 325 N west on the sailboat. What is the magnitude and direction of the net force on the sailboat?

Nov 8, 2015

Direction = ${45}^{o}$ North of West (Due North-West)
Magnitude = 557 N

#### Explanation:

In this question you have a force (452N) due North and a force (325N) due West. Since these directions are ${90}^{o}$ apart from one another the angle of the net force is ${45}^{o}$.

To calculate the magnitude you must reach WAAAAAY back in your math classes to the pythagorean theorem; since you can view these vectors as a triangle with the net force being the hypotenuse.
${a}^{2} + {b}^{2} = {c}^{2}$
${\left(325 N\right)}^{2} + {\left(452 N\right)}^{2} = 309929 {N}^{2}$

You can then take the square root of your answer to find the magnitude in Newtons.

$\sqrt{309929 {N}^{2}} = 557 N$