# Three men are pulling on ropes attached to a tree the ﬁrst man exerts a force of 6.0 N north, the second a force of 35 N east, and the third 40 N to south. What is the magnitude of the resultant force on the tree?

Dec 1, 2015

$48.8 \text{N}$ on a bearing of ${134.2}^{\circ}$

#### Explanation:

First we can find the resultant force of the men pulling in the north and south directions:

$F = 40 - 6 = 34 \text{N}$ due south (180)

Now we can find the resultant of this force and the man pulling east.

Using Pythagoras:

${R}^{2} = {34}^{2} + {35}^{2} = 2381$

$\therefore R = \sqrt{2381} = 44.8 \text{N}$

The angle $\theta$ from the vertical is given by:

$\tan \theta = \frac{35}{34} = 1.0294$

$\therefore \theta = {45.8}^{\circ}$

Taking N as zero degrees this is on a bearing of ${134.2}^{\circ}$