Answer to Question #251477 in Mechanics | Relativity for Max

Question

Considering vector A = 100 N, directed to the East and vector B = 75 N, 60° from positive x-axis, capture the image of the resultant vector A - B. Then, try to find the resultant vector using the Law of Sines and Cosines

Answer 1

Explanations & Calculations

• Angle POQ = 60 degrees.
• To calculate the magnitude of PQ, apply cosine law to POQ triangle.

$\qquad\qquad \begin{aligned} \small \cos 60 &=\small \frac{100^2+75^2-PQ^2}{2\times75\times100}\\ \small PQ^2 &=\small 8125 \,N^2\\ \small PQ &=\small 25\sqrt{13}\,N \end{aligned}$

• To find the direction of the resultant vector, consider the vector addition on the POQ triangle,

$\qquad\qquad \begin{aligned} \small \vec{PQ}&=\small \vec{PO}+\vec{OQ}\\ &=\small (-\vec{B})+\vec{A}\\ &=\small \vec{A}-\vec{B} \end{aligned}$

• Direction is from P to Q.