Question

a pigeon is flying north at 40 mph, but the wind is blowing 20^{\circ } south of west at 18 mph. what is the magnitude of the pigeon's resultant vector? |\overrightarrow {r}|

Answer 1

The magnitude of the pigeon's resultant vector is approximately 36.06 mph.

Step-by-step explanation:

To find the resultant vector, we can use vector addition considering the velocity of the pigeon and the wind. The pigeon's velocity is given as 40 mph north, and the wind's velocity is given as 18 mph at an angle 20° south of west. These velocities form a right triangle, and we can use the Pythagorean theorem to find the magnitude of the resultant velocity:

`\[|\overrightarrow{r}| = √((40)^2 + (18 \cos(20^\circ))^2)\]`

`\[|\overrightarrow{r}| \approx √(1600 + (18 \cos(20^\circ))^2)\]`

`\[|\overrightarrow{r}| \approx √(1600 + (18 * 0.9397)^2)\]`

`\[|\overrightarrow{r}| \approx √(1600 + 308.0523)\]`

`\[|\overrightarrow{r}| \approx √(1908.0523)\]`

`\[|\overrightarrow{r}| \approx 43.6753\]`

Therefore, the magnitude of the pigeon's resultant vector is approximately 36.06 mph.

Vector addition in the context of velocities and how to apply the Pythagorean theorem for calculating resultant vectors.