A boat is traveling on a bearing of 25 degrees East of North at a speed of 4 knots (a knot is 1.852 km/h). After traveling for 3 hours, the boats heading is changed to due South and it travels for an additional 2 hours at 5 knots. Using a Vector diagram, what is the resultant?
Hi, I am completely new to this, and missed a lot of classes due to hospital trips. Trying to cathc up but there is no sample question in my text. I don't really know how to get the numbers to make the vectors. Can you lead me in the right direction, would be very much appreciated, thank yo very much.
Of course! I'd be happy to guide you through the steps to solve this problem.
To create a vector diagram, you'll need to break down the boat's motion into its component vectors. Let's start with the first leg of the journey, where the boat is traveling on a bearing of 25 degrees East of North at a speed of 4 knots for 3 hours.
1. Determine the magnitude and direction of the first vector:
- Since the speed is given in knots, we need to convert it to km/h. One knot is equal to 1.852 km/h.
- The boat's speed is 4 knots, so the magnitude of the first vector is 4 knots * 1.852 km/h = 7.408 km/h.
- The direction of the first vector is 25 degrees East of North.
2. Draw the first vector:
- Start at the origin (representing the starting point of the boat).
- Draw an arrow that represents the magnitude and direction of the first vector, which is 7.408 km/h and 25 degrees East of North.
Now let's move on to the second leg of the journey, where the boat changes its heading to due South and travels for an additional 2 hours at a speed of 5 knots.
3. Determine the magnitude and direction of the second vector:
- Convert the speed from knots to km/h: 5 knots * 1.852 km/h = 9.26 km/h.
- The direction of the second vector is due South, which is 180 degrees.
4. Draw the second vector:
- Start the second vector from the endpoint of the first vector (the tip of the arrow you drew for the first vector).
- Draw an arrow that represents the magnitude and direction of the second vector, which is 9.26 km/h and due South.
5. Find the resultant vector:
- To find the resultant vector, you need to add the two vectors together.
- To add them graphically, connect the starting point of the first vector to the endpoint of the second vector.
- The resulting line connecting the two points represents the resultant vector.
6. Measure the magnitude and direction of the resultant vector:
- Measure the length of the resultant vector.
- Measure the angle between the resultant vector and North (or whichever reference direction you prefer).
Remember to carefully label your vector diagram and use appropriate units for the magnitudes.
I hope this helps you get started with creating the vector diagram for this problem. If you have any further questions, feel free to ask!