Chapter 8.1, Problem 31E

To determine

To find: the magnitude of horizontal and vertical components of $\overrightarrow{r}$ .

Answer to Problem 31E

  $\begin{array}{l}h=-1.6\text{ cm}\\ v=2.05\text{ cm}\end{array}$

Explanation of Solution

Given information:

The magnitude and direction of given vector is as follows:

  $\begin{array}{l}\text{Magnitude}=2.6\text{ cm}\\ \text{Direction}=128°\end{array}$

Calculation:

Let the horizontal and vertical component be $h$ and $v$ respectively.

The horizontal component of the vector is evaluated as follows:

  $\begin{array}{c}h=\text{magnitude}\times \text{cos}\left(\text{direction}\right)\\ =2.6\cos \left(128°\right)\left[\text{Put the value of magnitude and direction}\right]\\ =-1.6\text{ cm}\end{array}$

The vertical component of the vector is evaluated as follows:

  $\begin{array}{c}v=\text{magnitude}\times \sin \left(\text{direction}\right)\\ =2.6\sin \left(128°\right)\left[\text{Put the value of magnitude and direction}\right]\\ =2.05\text{ cm}\end{array}$

Thus the horizontal and vertical component of the given vector is $-1.6\text{ cm}$ and $2.05\text{ cm}$ respectively.