A force `vec F_(1)` of magnitude 9 N makes an angle of `30^(@)` with the X-axis. Another force `vec F_(2)` of magnitude 12 N, makes an angle of `120^(@)` with the X-axis. What is the magnitude of the resultant force ?

Options

A. 7.5 N
B. 10 N
C. 12.5 N
D. 15 N

Answer

D

Explanation

Forces `vec F_(1) and vec F_(2)` are inclined at `30^(@) and 120^(@)` respectively to the x-axis i.e. the angle between them = `120^(@) -30^(@) =90^(@)`
Since `vec F_(1) and vec F_(2)` are perpendicular, the magnitude of the resultant force is
`F = sqrt (F_(1)^(2) + F_(2)^(2))`
`=sqrt (9^(2) +12^(2)) = sqrt (81+144) = sqrt(225)`
`therefore F= 15 N`