Question

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 40° 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

magnitude= 180.278 pounds
((75 3/-50)^2+ (75+50 3)^2)
352500
50 13

direction= 63.90
tan^-1 (( 75+50 3)/(75 3-50))
where you see the big spaces I mage put the check mark symbol

Answer 2

Resultant force =115.03 pounds

Direction of resultant force=81.8 degrees

Explanation:

We are given that two forces

Let
`F_1=150 pounds`

`F_2=100 pounds`

`\theta_1=40^(\circ)`

`\theta_2=170^(\circ)`

`Sin(40^(\circ))=(vertical component )/(hypotenuse )`

`0.643=(vertcal component )/(150)`

Vertical component of force
`F_0.643* 150=96.45`

Horizontal component =
`100cos (40^(\circ))=150*0.766=114.9`

Vertical component of second force
`F_2= 100* sin170=100* 0.174=17.4`

Horizontal component of force
`F_2=100cos 170=100* (-0.985)=-98.5`

Vertical component of resultant force=96.45+17.4=113.85

Horizontal component of resultant force=114.9-98.5=16.4

Magnitude of resultant force =
`√((113.85)^2+(16.4)^2)=√(12961.8225+268.96)=√(13230.7825)`=115.03 pounds

Direction =
`tan^(-1)((vertical component)/(horizontal component))`

Direction of resultant vector force=
`tan^(-1)((113.85)/(16.4)=tan^(-1)(6.94)`=81.8 degrees