Question

A pigeon is flying north at 40mph, but the wind is blowing 20 degrees south of west at 18mph. magnitude 37.84 mph. what is the direction of the pigeon's resultant vector?

Answer 1

The pigeon's resultant vector is 42.43 mph in a direction 22.9 degrees south of west.

Step-by-step explanation:

To find the direction of the pigeon's resultant vector, we need to break down the velocities into their components. The pigeon is flying north at 40 mph, so its northward component is 40 mph. The wind is blowing 20 degrees south of west at 18 mph, so its westward component is 18 mph * cos(20 degrees) = 16.67 mph and its southward component is 18 mph * sin(20 degrees) = 6.03 mph.

Next, we add the components together. The northward component of the pigeon and the southward component of the wind cancel each other out, so we are left with a westward component of 16.67 mph. The resultant vector is the hypotenuse of the right triangle formed by the westward component and the northward component of the wind. We can find its magnitude using the Pythagorean theorem: sqrt((40 mph)^2 + (16.67 mph)^2) = 42.43 mph.

The direction of the resultant vector can be found using the inverse tangent function: arctan((16.67 mph)/(40 mph)) = 22.9 degrees south of west. Therefore, the direction of the pigeon's resultant vector is 22.9 degrees south of west.