Question

A hiker sets out for a long hike. The first leg of the hike he walks at an angle of 25° north of east and walks for 450 km. Then the hiker tums an angle of 38 south of east and walks 510 km. From there the hiker turns at an angle of 22° west of south and walks 550 km. What would be the most direct route from the hiker's starting position to final position? (Labeled the resultant vector)

Answer 1

To find the most direct route, calculate the resultant vector by adding up the individual vectors and determining the magnitude and direction of the resultant vector.

Step-by-step explanation:

To find the most direct route from the hiker's starting position to the final position, we need to determine the resultant vector, which is the sum of all the individual vectors. Here's how:

1. Start by drawing the vectors on a graph, with the lengths of each vector representing the distances walked.
2. Label the vectors with their respective angles and distances.
3. Use trigonometry to find the horizontal and vertical components of each vector.
4. Add up the horizontal and vertical components separately to find the total horizontal and vertical displacements.
5. Use the Pythagorean theorem to find the magnitude of the resultant vector by taking the square root of the sum of the squares of the horizontal and vertical displacements.
6. Finally, use trigonometry to find the direction of the resultant vector by taking the inverse tangent of the vertical displacement divided by the horizontal displacement.

By following these steps, you'll be able to find the most direct route from the hiker's starting position to the final position.