A body of mass $m=1\text{ kg}$ is acted upon by two perpendicular forces of $F_1=3\text{ N}$ and $F_2=4\text{ N}$. What is the magnitude of the acceleration $a$ of the body?

Solution

1. Given the mass $m=1\text{ kg}$ and two perpendicular forces $F_1=3\text{ N}$ and $F_2=4\text{ N}$.
2. Calculate the net force $F_{\text{net}}$ using the Pythagorean theorem: $$\begin{array}{rl}{F}_{\text{net}}& =\sqrt{F_1^2+F_2^2}\\ & =\sqrt{3^2+4^2}\\ & =\sqrt{9+16}\\ & =5\text{ N}\end{array}$$.
3. Apply Newton's second law, $F=ma$, to find the acceleration: $$\begin{array}{rl}a& =\frac{F_{\text{net}}}{m}\\ & =\frac{5\text{ N}}{1\text{ kg}}\\ & =5{\text{ m/s}}^2\end{array}$$.
4. Hence the answer is (A).