How Do You Calculate a Ship's Velocity Given Its Direction and Displacement?

[Below]

Homework Statement

A ship traveling 55 degrees [W of N] is 65.0 km farther north after 3.0 h. What is the ship's velocity?

Homework Equations

N/A

The Attempt at a Solution

I am totally not sure how to start this problem. My teacher told me there are two type of problems, AIM or Drift. I think this problem is AIM. I know then I have to draw the resultant first.

 

[dynamicsolo]

Homework Statement

A ship traveling 55 degrees [W of N] is 65.0 km farther north after 3.0 h. What is the ship's velocity?

This is a problem involving components of the velocity vector. Draw the direction of the velocity vector, which points 55º west of north. Then draw its northward and westward components so that you've formed a right triangle.

You are told that the ship is 65 km farther north after 3 hours, so what is the northward component of the ship's velocity (the speed in the northerly direction)? How can you use trigonometry to find the length of the hypotenuse of this triangle, which represents the total magnitude of the ship's velocity? (You already know the direction.)

 

[Moetasim]

I would approach this problem by first identifying the given information and what is being asked. We are given the direction of the ship's travel (55 degrees W of N) and the change in its position (65.0 km farther north). We are asked to find the ship's velocity.

Next, I would draw a diagram to visualize the situation. The ship's initial position can be represented by the origin of the diagram, and the direction of travel can be represented by an arrow pointing 55 degrees west of north. The change in position can be represented by another arrow pointing directly north. The resultant of these two arrows will represent the ship's velocity.

To find the magnitude of the velocity, we can use the Pythagorean theorem to calculate the length of the resultant vector. The direction of the velocity can be found by using trigonometric functions to find the angle between the resultant vector and the north direction.

Using the given information and the calculated magnitude and direction of the velocity, we can then provide a complete response to the problem. It is important to note that this solution assumes the ship traveled at a constant velocity for the entire 3.0 hours. If this is not the case, further information or assumptions may need to be made in order to accurately solve the problem.