Question

A drone is flying at a speed of 40 miles per hour in the direction of S 70° W. There is a wind of 15 miles per hour in the direction of S 10° E. Find the resultant magnitude and direction (as a quadrant bearing) of the drone.

Answer 1

To find the resultant velocity of the drone affected by the wind, vector components of the drone and wind velocities are summed, and then the magnitude and direction of the resultant vector are calculated using the Pythagorean theorem and trigonometric functions.

Step-by-step explanation:

The question involves the application of vector addition to calculate the resultant velocity of a drone that is affected by wind velocity. To find the resultant magnitude and direction, we need to break down the drone and wind velocities into their component vectors and then combine these components. Both vectors are given in quadrant bearings, so they must be converted into standard bearing or Cartesian coordinates for calculation. Once the components are summed, we can calculate the magnitude of the resultant vector using the Pythagorean theorem and find its direction using inverse trigonometric functions to determine the angle.

Graphical methods such as drawing or using a computer program can also be helpful to visually represent the vectors and their resultant. This involves sketching the vectors based on their magnitude and direction, forming a parallelogram, and then measuring the diagonal, which represents the resultant vector.