Question

Nancy is running some errands. Her first stop is 83km to the east and 51km to the north from her house. Her second stop is 37km to the west and 23km to the south from her first stop. Her third stop is 14km to the east and 3km to the south from her second stop. At her third stop, Nancy is exactly 65 km from her home. What is Nancy's direction relative to her starting point (home) once she arrives at her third stop?

1) Northwest
2) Northeast
3) Southwest
4) Southeast

Answer 1

Nancy's direction relative to her starting point (home) once she arrives at her third stop is northeast.

Step-by-step explanation:

To find Nancy's direction relative to her starting point (home) once she arrives at her third stop, we can use vector addition.

Let's break down each leg of the journey into vectors:

1. Her first stop is 83 km east and 51 km north from her home, which can be represented as a vector of (83, 51).
2. Her second stop is 37 km west and 23 km south from her first stop, which can be represented as a vector of (-37, -23).
3. Her third stop is 14 km east and 3 km south from her second stop, which can be represented as a vector of (14, -3).

To find the total displacement from her home to her third stop, we add these vectors together:

(83, 51) + (-37, -23) + (14, -3) = (60, 25)

Therefore, Nancy's direction relative to her starting point once she arrives at her third stop is northeast.