Question

A body of mass $5kg$ is acted upon by two perpendicular force $8N$ and $6N$, find the magnitude and direction the acceleration

• A. $3{ms}^{-2},\theta ={\cos }^{-1}\left(0.8\right)$ from $8m$
• B. $2{ms}^{-2},\theta ={\cos }^{-1}\left(0.6\right)$ from $6m$
• C. $3{ms}^{-2},\theta ={\cos }^{-1}\left(0.9\right)$ from $6m$
• D. $5{ms}^{-2},\theta ={\cos }^{-1}\left(0.8\right)$ from $8m$

Answer 1

The correct option is B $2{ms}^{-2},\theta ={\cos }^{-1}\left(0.6\right)$ from $6m$

Net force: $F=\sqrt{F_1^2+F_2^2+F_1{F}_2\cos \theta }$

$F=\sqrt{64+36+0}=\sqrt{10}N$

Acceleration, $a=\frac{F}{m}=\frac{10}{5}=2m/s^2$