Question

If an airplane is flying directly north at 300.0 km/h, and a crosswind is hitting the airplane at 50.0 km/h from the east, what is the airplane's resultant velocity?

Answer 1

If an airplane is flying directly north at $300.0 \, \text{km/h}$ , and a crosswind is hitting the airplane at $50.0 \, \text{km/h}$ from the east, what is the airplane's resultant velocity?

Solution.

The resultant velocity $\overrightarrow{v_r}$ is the vector addition of the airplane's velocity $\overrightarrow{v_a}$ and the crosswind's velocity $\overrightarrow{v_c}$ . The vector addition is given by the parallelogram law and the module $|\overrightarrow{v_r}|$ is given by Pythagora's theorem: $|\overrightarrow{v_r}| = \sqrt{|\overrightarrow{v_a}|^2 + |\overrightarrow{v_c}|^2} = \sqrt{300^2 + 50^2} = 304.14 \, \text{km/h}$ . The direction of the resultant velocity is the Northwest.

Answer: $304.14\mathrm{km / h}$