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?

Question

Hi, I am completely new to this, and missed a lot of classes due to hospital trips. Trying to catch up but there is no sample question in my text like this one. 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 you very much. Do I convert the knots km/hr then divide that by the time (hours) for displacement, then use that number for the vectors?

Answer 1

no need to convert knots to km/hr. Just work with knots, and your final answer will be in knots.

For problems like this, it's always helpful to draw a diagram to visualize what's going on.

You will need to take sin/cos of the angles to get the x- and y-components of the velocities. Then you add them up separately to get the resultant vectors.

Also, boats don't travel on bearings; they travel on headings. If they are going toward a distant point, the direction toward that point is the bearing of the point. The heading of the boat is the bearing of the point, only if it is going directly toward the point. If the point is west of the boat, then if the boat is on a heading of due north, the bearing of the point is constantly changing.

So. The boat travels for 3 hours at 4 knots, going a distance of 12 nautical miles.

12 @ N25°E = (5.07,10.88)
10 @ S = (0,-10)

Add them up to get a final position of (5.07,-0.88)

Convert that back to distance and heading to get 5.15 @ E10°S

Remember that the x- and y-components of a vector in direction x° (measured from North) are d*sin(x) and d*cos(x)

Given an (x,y) position, d=√(x^2+y^2) and the direction is 90°-arctan(y/x)

You may see other formulas, but they will resolve to the same values. Use the formulas you feel most comfortable working with.

Answer 2

Hi Steve, thank you. The answer for the question 81.4N at 84 degrees west of north or 6 degrees north of west. But they show no work to get the answer. I am still confused, please help me a little more. Thanks
Steve.

Answer 3

Sorry Steve wrong answer, they got 60.5 degrees east of north or 29.5 degrees north of east. Sorry about that.

Answer 4

the resultant is 54.7 degrees.... i only know that cause im stuck on the same question and have the answer sheet... i have no idea how to do a vector graph. im slowly going crazy myself..