Chapter 8, Problem 18SGA

To determine

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

Answer to Problem 18SGA

  $\begin{array}{l}h=2.86\text{ cm}\\ v=0.5\text{ cm}\end{array}$

Explanation of Solution

Given information:

The magnitude and direction of given vector is as follows:

  $\begin{array}{l}\text{Magnitude of }\overrightarrow{q}=2.9\text{ cm}\\ \text{Direction of }\overrightarrow{q}=10°\end{array}$

Calculation:

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

The horizontal component of the vector is evaluated as follows:

  $\begin{array}{l}h=\text{magnitude}\times \text{cos}\left(\text{direction}\right)\\ =2.9\cos \left(10°\right)\left[\text{Put the value of magnitude and direction}\right]\\ =2.86\text{ cm}\end{array}$

The vertical component of the vector is evaluated as follows:

  $\begin{array}{c}v=\text{magnitude}\times \sin \left(\text{direction}\right)\\ =2.9\sin \left(10°\right)\left[\text{Put the value of magnitude and direction}\right]\\ =0.5\text{ cm}\end{array}$

Thus the horizontal and vertical component of the given vector is $\text{2}\text{.86 cm}$ and $0.5\text{ cm}$ respectively.