Chapter 3, Problem 16P

To determine

The two possibilities for x component

Answer to Problem 16P

+43.30 and − 43.30

Explanation of Solution

Given:

Inx-y plane, vector has magnitude of 70 units and y component has magnitude − 55 units.

  $\begin{array}{l}\text{Magnitude,}\left|\overrightarrow{A}\right|=70\text{ units}\\ y\text{ component,}\left|\overrightarrow{y}\right|=-55\text{ unit}\end{array}$

Formula Used:

Resultant of vector is,

  $\left|\overrightarrow{A}\right|=\sqrt{x^2+y^2}$

Calculation :

Substituting, the given values

  $70=\sqrt{x^2+y^2}$

Squaring on both sides,

  $\begin{array}{l}{\left(70\right)}^2=x^2+y^2\\ {\left(70\right)}^2=x^2+{\left[-55\right]}^2\\ x^2={\left(70\right)}^2+{\left[-55\right]}^2\\ x^2=4900-3025\\ x^2=1875\\ x=\pm 43.30\\ x=+43.30,-43.30\end{array}$

Conclusion :

Thus, the two possibilities of x components are + 43.30 and − 43.30