Chapter 8.1, Problem 41E

To determine

To find: the horizontal and vertical components of car’s velocity.

Answer to Problem 41E

  $\begin{array}{l}h=36\text{ mph}\\ v=30\text{ mph}\end{array}$

Explanation of Solution

Given information:

The magnitude and direction of car vector is as follows:

  $\begin{array}{l}\text{Magnitude}=47\text{ mph}\\ \text{Direction}=40°\end{array}$

Calculation:

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

The horizontal component of the vector is evaluated as follows:

  $\begin{array}{c}h=\text{magnitude}\times \text{cos}\left(\text{direction}\right)\\ =47\cos \left(40°\right)\left[\text{Put the value of magnitude and direction}\right]\\ =36\text{ mph}\end{array}$

The vertical component of the vector is evaluated as follows:

  $\begin{array}{c}v=\text{magnitude}\times \sin \left(\text{direction}\right)\\ =47\sin \left(40°\right)\left[\text{Put the value of magnitude and direction}\right]\\ =30\text{ mph}\end{array}$

Thus the horizontal and vertical component of the given vector is $36\text{ mph}$ and $30\text{ mph}$ respectively.