Buried Treasure Adventure: Sam and Joe's Journey

What is the magnitude and direction of the vector from Sam to Joe?

Find the magnitude and direction of the vector from Sam to Joe.

Answer:

The magnitude of the vector from Sam to Joe is approximately 23.71 m, and the direction is approximately 49.4 degrees with the west-to-east direction.

Two boys, Joe and Sam, went on an adventure to search for buried treasure. They started underneath the same tree and walked in different directions. Joe walked 15 m east and then 18 m north, while Sam walked 15 m west and then 12 m south. After their journey, both boys stopped at their respective positions.

To find the vector from Sam to Joe, we can calculate the difference in their positions. Joe's final position is 15 m east and 18 m north from the starting point, while Sam's final position is 15 m west and 12 m south from the starting point.

To determine the magnitude of the vector, we can use the Pythagorean theorem:

Magnitude = sqrt((15 m)^2 + (18 m)^2) ≈ 23.71 m

To express the direction of the vector, we can find the angle it makes with the west-to-east direction using trigonometry:

Angle = arctan((18 m) / (15 m)) ≈ 49.4 degrees

By calculating these values, we can determine that the magnitude of the vector from Sam to Joe is approximately 23.71 m, and the direction is approximately 49.4 degrees with the west-to-east direction.