Question

Components of a Velocity

A jet is flying in a direction $N20°E$ with a speed of $500mi/h$. Find the north and east components of the velocity

Short answer

The east component of the velocity$V_{east}=469.5mi/h$and the north component of the velocity is $V_{north}=171mi/h$

Step-by-step solution

Step 1. Given information

A jet is flying with velocity of $500mi/h$ in the direction of $N{20}^{°}E$

Step 2. Concept used

First we have to write velocity into vector form. To do this, we need direction and the modulus of vector. A vector in component form can be written as-

$v=a_{1}i+a_{2}j$

Where $a_1=\left|v\right|\cos \theta \&a_2=\left|v\right|\sin \theta$

$a_1$ is the horizontal component and $a_2$is the vertical component. And we know that we take North is in vertical direction.

Step 3. Calculation

East component of velocity can be written as-

$\begin{array}{l}{V}_{east}=\left|V\right|\cos \theta \\ V_{\text{east}}=500\cos {20}^{°}\\ \approx 500\cdot 0.939\\ =469.5\end{array}$

And the north component is-

$\begin{array}{l}{V}_{north}=\left|V\right|\sin \theta \\ V_{\text{north}}=500\sin {20}^{°}\\ \approx 500\cdot 0.342\\ =171\end{array}$