Chapter 5.1, Problem 11SSC

To determine

The components of the vector M.

Answer to Problem 11SSC

  $M_x=3.99$ and $M_y=3.00$

Explanation of Solution

Given:

The magnitude of vector M is $5.0$ .

Angle made of vector M from the horizontal, $\theta ={37.0}^{\text{o}}$

Formula used:

The rectangular components of a vector A making an angle of $\theta$ with the horizontal axis or x-axis, are:

  $A_x=A\cos \theta$

  $A_y=A\sin \theta$

Calculation:

Thus, the first component of the vector M will be:

  $\begin{array}{c}{M}_x=M\cos 37°\\ =5\cos 37°\\ =3.99\end{array}$

And, the second component will be:

  $\begin{array}{c}{M}_y=M\sin 37°\\ =5\sin 37°\\ =3.00\end{array}$

Conclusion:

Thus, the horizontal and the vertical component of the vector Mwill be 3.99 and 3.00, respectively.