What is the total displacement for a boat that sails 200m [S25W] and then changes course and sails 150m [N30E]?

Answer 1

To calculate the total displacement, we need to find the resultant displacement by adding the two vectors.

The first vector is 200m [S25W].

Let's break it down into horizontal (x) and vertical (y) components:

Horizontal component: 200m * cos(25°) = 181.04m [W]
Vertical component: 200m * sin(25°) = 85.47m [S]

The second vector is 150m [N30E].

Let's break it down into horizontal (x) and vertical (y) components:

Horizontal component: 150m * cos(30°) = 129.9m [E]
Vertical component: 150m * sin(30°) = 75m [N]

Now, we can add the horizontal and vertical components separately:

Horizontal displacement: 181.04m [W] + 129.9m [E] = 51.14m [E]
Vertical displacement: 85.47m [S] + 75m [N] = 10.47m [S]

Therefore, the total displacement is 51.14m [E] with a small south component of 10.47m [S].