Find the magnitude and direction of a force, if its x-component

E

Editor

Jun 20, 2022

Find the magnitude and direction of a force, if its x-component is 12 N and y-component is 5 N. (13 N making 22.6⁰ with x-axis)

Solution:$F_{x}$ = 12 N $F_{y}$= 5 N Magnitude of the force = F = ?Direction of the force = θ = ? F = $√F_{x}^{2} + F_{y}^{2}$ F = $√(12)^{2} + (5)^{2}$ F = √144+25 F = 13 N  θ = $tan^{-1} =\frac{F_{y}}{F_{x}}$ θ = $tan^{-1} =\frac{12}{5}$  θ = $tan^{-1}$ (2.4) θ = 22.6⁰ with x-axis