Chapter 9.4, Problem 54SPR

(a)

To determine

To find: The resultant vector.

Answer to Problem 54SPR

The resultant vector is $\left(-350,450\right)\text{mph}$ .

Explanation of Solution

Given:

A jet is flying northwest and its velocity is <-450, 450> miles per hour.

The wind from the west and its velocity is <100, 0> miles per hour.

Calculation:

The required diagram is shown in below figure:

  

Calculate the resultant vector.

  $\begin{array}{c}\overline{r}=\left(-450,450\right)+\left(100,0\right)\\ =\left(-350,450\right)\text{mph}\end{array}$

Thus, the resultant vector is $\left(-350,450\right)\text{mph}$ .

(b)

To determine

To find: The magnitude.

Answer to Problem 54SPR

The magnitude is $570.1$ .

Explanation of Solution

Given:

A jet is flying northwest and its velocity is <-450, 450> miles per hour.

The wind from the west and its velocity is <100, 0> miles per hour.

Calculation:

Calculate the magnitude.

  $\begin{array}{c}m=\sqrt{{\left(-350\right)}^2+{\left(450\right)}^2}\\ =\sqrt{122500+202500}\\ =570.1\end{array}$

Thus, the magnitude is $570.1$

(c)

To determine

To find: The direction

Answer to Problem 54SPR

The direction is $52.1$ above the negative axis.

Explanation of Solution

Given:

A jet is flying northwest and its velocity is <-450, 450> miles per hour.

The wind from the west and its velocity is <100, 0> miles per hour.

Calculation:

Calculate the direction.

  $\begin{array}{c}\tan \theta =\frac{450}{350}\\ \theta ={\tan }^{-1}\left(\frac{9}{7}\right)\\ =52.1°\end{array}$

Thus, the direction is $52.1$ above the negative axis.