Find the resultant of the following forces.
`[sin 37^(@) = (3)/(5) ,cos 37^(@) = (4)/(5) , sin 53^(@) = (4)/(5) , cos 53^(@) = (3)/(5)]`

Options

A. The resultant of these is 10N at`53^(@)`with the positive X-axis.
B. The resultant of these is 10N at`43^(@)`with the positive X-axis.
C. The resultant of these is 100N at`53^(@)`with the positive X-axis.
D. The resultant of these is 120N at`53^(@)`with the positive X-axis.

Answer

A

Explanation

Resolve the inclined vectors.

Now combine the components in x and directions, by taking the proper sing.
`F_(x)=4-6+8=6`
`and F_(y)=3+8-3=8`
resultant force ', `F=sqrt((6)^(2)+(8)^(2)=10N)`
Direction of force,tantheta`=(F_(y))/(F_(x))=(8)/(6)=(4)/(3)impliestheta=53^(@)`

The resultant of these is 10N at`53^(@)`with the positive X-axis.