Chapter 9.1, Problem 54E

To determine

To find: The east and north components of the velocity of flying jet.

Answer to Problem 54E

The east component of velocity of jet is $171.01\text{mi/h}$ and the north component of velocity of jet is $469.84\text{mi/h}$.

Explanation of Solution

Given:

The speed of jet is $500\text{mi/h}$ and direction of jet is $\text{N}20°\text{E}$.

Formula used:

The horizontal component ${\text{V}}_x$ of velocity V is,

${\text{V}}_x=\text{V}\cos \theta$ (1)

The vertical component ${\text{V}}_y$ of velocity V is,

${\text{V}}_y=\text{V}\sin \theta$ (2)

Where, $\theta$ is the angle made by velocity V with horizontal direction.

Calculation:

The figure below represents the velocity and direction of jet,

Figure (1)

Jet is flying in the direction $\text{N}20°\text{E}$.

Angle $\theta$ made by jet with east direction is calculated as,

$\begin{array}{c}\theta =90°-20°\\ =70°\end{array}$

So, angle $\theta$ made by jet with horizontal or east direction is $70°$.

Substitute $500$ for V, $70°$ for $\theta$ in equation (1), to calculate horizontal component ${\text{V}}_x$,

$\begin{array}{c}{\text{V}}_x=500\cos 70°\\ =500\times 0.3420\\ =171.01\end{array}$

Substitute $500$ for V, $70°$ for $\theta$ in equation (2), to calculate vertical component ${\text{V}}_y$,

$\begin{array}{c}{\text{V}}_y=500\sin 70°\\ =500\times 0.9396\\ =469.84\end{array}$

Thus, the horizontal or east component of velocity of jet is $171.01\text{mi/h}$ and the vertical or north component of velocity of jet is $469.84\text{mi/h}$.