Question

A jet aircraft is aimed south and travelling 851km/h. A wind blows the plane from 40 degrees N of E at 36km/h. What is the plane's resultant velocity?

Answer 1

A jet aircraft is aimed south and travelling $851\mathrm{km/h}$ . A wind blows the plane from 40 degrees N of E at $36\mathrm{km/h}$ . What is the plane's resultant velocity?

Solution:

The resultant velocity is as vector sum:

$$\vec {v} (\text {resultant}) = \vec {v} (\text {aircraft}) + \vec {v} (\text {wind})$$

According to the parallelogram rule:

$$\begin{array}{l} | \vec {v} (\text {resultant}) | = \\ \sqrt {| \vec {v} (\text {aircraft}) | ^ {2} + | \vec {v} (\text {wind}) | ^ {2} + 2 | \vec {v} (\text {aircraft}) | * | \vec {v} (\text {wind}) | * \cos \alpha} \\ \end{array}$$

Were $\alpha$ is the angle between the vectors

$$\alpha = 9 0 ^ {0} + 4 0 ^ {0} = 1 3 0 ^ {0}$$ $$| \vec {v} (\text {resultant}) | = \sqrt {8 5 1 ^ {2} + 3 6 ^ {2} + 2 * 5 8 1 * 3 6 * \cos (1 3 0 ^ {0})}$$ $$| \vec {v} (\text {resultant}) | = 8 2 8, 3 2 \mathrm {k m} / \mathrm {h}$$

Answer: the resultant velocity is $828 \, \text{km/h}$ .