The following force vectors act on an object: i)50.0 newtons at 45.0 $\degree$ north of east and ii)25.0 newtons at 30.0 $\degree$ south of east.Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?
A)75.0 newtons 7.50 $\degree$
B)61.4 newtons 21.8 $\degree$
C)23.4 newtons 18.3 $\degree$
D)12.8 newtons 37.5 $\degree$

Question

Quizplus · Accepted Answer

To find the resultant force, we can use the Pythagorean theorem to add the two vectors together: 
$F_{R} = \sqrt{(50 \cos(45^{\circ}) - 25 \cos(30^{\circ}))^2 + (50 \sin(45^{\circ}) + 25 \sin(30^{\circ}))^2} \approx 61.4$ N

To find the angle the resultant vector makes with the easterly direction, we can use the inverse tangent function: 
$	heta = 	an^{-1}(\frac{50 \sin(45^{\circ}) + 25 \sin(30^{\circ})}{50 \cos(45^{\circ}) - 25 \cos(30^{\circ})}) \approx 21.8^{\circ}$ south of east

Therefore, the best choice is B: 61.4 newtons 21.8° south of east.

The Following Force Vectors Act on an Object: I)50 °\degree° North of East and Ii)25

The Following Force Vectors Act on an Object: I)50 $\degree$ North of East and Ii)25