Answer
Acceleration $\vec{a}$ has magnitude of $18.03m/s^2$ and is directed at an angle of $56.3^o$ to the x axis.
Work Step by Step
We will solve this problem using unit-vector notation.
First, rewrite the two forces in unit-vector notation.
- Force on x axis: $\vec{F}_x=40Ni$7
- Force on y axis: $\vec{F}_y=60Nj$
As a result, $\sum \vec{F}=40Ni+60Nj$
According to Newton's 2nd Law: $$\sum \vec{F}=m_{obj}\vec{a}$$ $$\vec{a}=\frac{\sum \vec{F}}{m}=\frac{40Ni+60Nj}{4kg}=10m/s^2i+15m/s^2j$$
- Magnitude: $a=\sqrt{10^2+15^2}=18.03m/s^2$
- Direction: let's call $\theta$ the angle of $\vec{a}$ relative to the x axis.
$$\tan\theta=\frac{15}{10}=1.5$$ $$\theta=56.3^o$$
