Chapter 6, Problem 10PS

(a)

To determine

To Find: The vector $u$ and $v$ in component form.

Answer to Problem 10PS

The magnitude of the vector $u=-120\text{j}$ and $v=40$ .

Explanation of Solution

Given:

The velocity of the skydiver falls at a constant downward velocity of $120\text{miles}\text{per}\text{hour}$ .

The breeze pushes the skydiver to the east at 40 miles per hour.

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

As the skydiver falls down in the positive direction and horizontally east in the positive direction $u\left(120,0\right),v\left(0,40\right)$ .

Thus, the magnitude of the vector $u=-120\text{j}$ and $v=40$ .

(b)

To determine

To Find: The value of the sum $s=u+v$ and the sketch for $s$ .

Answer to Problem 10PS

The value of sum is $40i-120j$ and sum is shown in Figure 2

Explanation of Solution

From the given figure the sum $s=u+v$ is calculated as,

  $\begin{array}{c}s=u+v\\ =40i-120j\end{array}$

The graph for the above sum is shown in Figure 2

  

Figure 2

(c)

To determine

To Find: The magnitude of $s$ and the effect of the wind is negligible in the sky driver’s fall.

Answer to Problem 10PS

The sum is $126.48\text{mph}$ and the effect of the wind is negligible in the sky diver’s fall.

Explanation of Solution

From the given figure the sum $s=u+v$ is calculated as,

  $\begin{array}{c}s=u+v\\ =40i-120j\end{array}$

Consider the magnitude of the above sum is,

  $\begin{array}{c}s=\sqrt{{\left(40\right)}^2+{\left(120\right)}^2}\\ =126.48\text{mph}\end{array}$

Thus, the sum is $126.48\text{mph}$ and the effect of the wind is negligible in the sky diver’s fall.

(d)

To determine

To Find: The angle to the ground that is the path of the skydiver when affected by the 40 mile per hour wind from due west.

Answer to Problem 10PS

The required angle is ${\tan }^{-1}71.57°$ .

Explanation of Solution

Given:

The speed of the wind is 40 miles per hour.

Calculation:

The required Figure is shown in Figure 2

  

Figure 2

Then, angle $\theta$ is obtained as,

  $\begin{array}{l}\tan \theta =\frac{120}{40}\\ \tan \theta =3\\ \theta ={\tan }^{-1}71.57°\end{array}$

(e)

To determine

To Find: The Figure that gives the visual representation of the problem and find the skydiver’s new velocity.

Answer to Problem 10PS

The required speed is $123.69\text{mph}$ and the required diagram is shown in Figure 1

Explanation of Solution

Given:

The constant downward velocity of the skydiver is 120 miles per hour and the speed to the west is 30 miles per hour.

Calculation:

The required diagram is shown in Figure3

  

Figure 3

Consider the magnitude of the speed is,

  $\begin{array}{c}s=\sqrt{{\left(30\right)}^2+{\left(120\right)}^2}\\ =123.69\text{mph}\end{array}$