Question

Find the magnitude and direction of (a) the resultant (b) the equilibrium of two forces, 10N acting in the direction N30east and 15 N acting in the easterly direction, if both forces act at a point

Answer 1

1)

$$\vec{R}=(10\cos{30},10\sin{30})+(15,0)\\=(23.66,5)\ N\\R=\sqrt{23.66^2+5^2}=24.2\ N\\ \theta=\arctan{\frac{5}{23.66}}=11.9\degree\text{ N of E}$$

2)

$$U=R=24.2\ N\\ \alpha=11.9\degree\text{ S of W}$$