Question

vector in two dimension.

• find the magnitude of the sum of two forces,

one 20.0 n and the other 7.0 n, when the angle
between them is 30.0°.

Explanation:

Step1: Recall the formula for the magnitude of the sum of two vectors

If we have two vectors \(\vec{A}\) and \(\vec{B}\) with magnitude \(A\) and \(B\) respectively and the angle \(\theta\) between them, the magnitude of their sum \(\vec{R}=\vec{A}+\vec{B}\) is given by \(R = \sqrt{A^{2}+B^{2}+2AB\cos\theta}\)

Here, \(A = 20.0\space N\), \(B=7.0\space N\) and \(\theta = 30.0^{\circ}\), \(\cos\theta=\cos30^{\circ}=\frac{\sqrt{3}}{2}\approx0.866\)

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Answer:

\(26.3\space N\)