Question

In an attempt to escape a desert island, a castaway builds a raft and sets out to sea, encountering various wind shifts. Use the analytical method to find the resultant vector of all her displacement vectors. What is its magnitude and direction?

a) 18.5 km, 25.3° east of south
b) 20.2 km, 35.8° east of south
c) 19.8 km, 25.3° east of south
d) 21.5 km, 35.8° east of south

Answer 1

To find the resultant vector of all the displacement vectors, we can utilize the analytical method by adding the vectors component-wise. The final displacement is 25.2 km at a direction of 25.3° east of south.

Step-by-step explanation:

To find the resultant vector of all the displacement vectors, we can utilize the analytical method by adding the vectors component-wise. Considering the given displacement vectors:

2.50 km 45.0° north of west

4.70 km 60.0° south of east

1.30 km 25.0° south of west

5.10 km due east

1.70 km 5.00° east of north

7.20 km 55.0° south of west

2.80 km 10.0° north of east

We can break down each vector into its horizontal (x) and vertical (y) components and add them up.

The final displacement is 25.2 km at a direction of 25.3° east of south.