Three forces with magnitudes 16 N, 12 N and 21 N are shown in the diagram below. Determine the magnitude of their resultant force and angle with the x-axis
Attached Figure / Diagram
A
7.63N,61°
B
8.71N,61°
C
7.63N,29°
D
8.71N,29°
Verified Correct Answer: B.
Physical Principles & Numerical Solution
Fx= 12cos32^\circ-16cos26^\circ = -4.20N (right is taken +ve and left is taken -ve)
Fy=12sin32^\circ+16sin26^\circ-21 = -7.63N (up is taken +ve and down is taken -ve)
\(R^2\)= 4.202+7.632
⇒\(R^2\) = 75.86
⇒ R=\sqrt75.86
∴R = 8.71 N
tan \theta=\(\frac{opp}{adj}\)
⇒tan \theta=\(\frac{7.63}{4.20}\)
⇒tan \theta =1.8095
⇒ \theta = \(tan^-1\) (1.8095)
\theta = 61^\circ
∴The angle of the resultant force with the x-axis is 61^\circ
Source: WAEC / JAMB / NECO Classroom Archive (Record #67919)