Question

Two forces with magnitudes of 200 and 100 pounds act on an object at angles of 60° and 170° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

We can find equals to the given components

`f1= 200cos(60), 200sin(60)`
Then you have to find equal for f2= 100cos(170) ,100sin(170) which is
`\ \textless \ -98.48, 17.36\ \textgreater \`
Substract the vectors to find F3 coordinates
`= \ \textless \ 1.52, 190.56\ \textgreater \`
`F3= \ \textless \ 100-98.48\ \textgreater \ , \ \textless \ 173.2+17.36\ \textgreater \`
With theese new coordinates it is possible to find the direction and magnitude by using arc tan and square rooting. You should make
`X= 1.52 and Y=190.56` and plug it to the arc tan function tan-
`1(190.56/1.52)`. You will obtain direction 89.54, then find magnitude of the square root of 36315.4 --
`(1.52)^2 + (190.56)^2`