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?

1 Answer
Dec 1, 2015

Answer:

#48.8"N"# on a bearing of #134.2^@#

Explanation:

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

#F=40-6=34"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#

#:.R=sqrt(2381)=44.8"N"#

The angle #theta# from the vertical is given by:

#tantheta=35/34=1.0294#

#:.theta=45.8^@#

Taking N as zero degrees this is on a bearing of #134.2^@#