Chapter 3, Problem 56GP

To determine

The y -component of a vector.

The direction of vector making an angle with x -axis.

Answer to Problem 56GP

  $v_y=46.37$

  31.6°

Explanation of Solution

Given:

  $\begin{array}{l}\text{Resultant vector magnitude in }xy\text{ plane, }{v}_p=88.5\\ \text{Vector component along }x\text{ axis, }{v}_x=75.4\end{array}$

Formula Used:

The resultant vector is given as,

  $\begin{array}{l}{v}_R{}^2=v_x^2+v_y^2\\ \cos \alpha =\frac{v_x}{v}\end{array}$

Calculation :

Substituting the values, to find the resultant vector.

  $\begin{array}{l}{v}_y=\sqrt{v_r^2-v_x^2}\\ v_y=\sqrt{{\left(88.3\right)}^2-{\left(75.4\right)}^2}\\ v_y=46.37\end{array}$

Substituting the values

  $\begin{array}{l}\cos \alpha =\frac{v_x}{v}\\ \cos \alpha =\frac{75.7}{88.5}\\ \alpha =31.6\end{array}$

Conclusion:

  $v_y=46.37$

  31.6°