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 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?
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.
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.
Sorry Steve wrong answer, they got 60.5 degrees east of north or 29.5 degrees north of east. Sorry about that.
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..
Yes, you're on the right track! To solve this problem, you need to break down the boat's motion into two separate vectors: one for the initial motion (25 degrees East of North at 4 knots) and another for the subsequent motion (due South at 5 knots).
To begin, let's convert the knot speed to km/h. Since 1 knot is equal to 1.852 km/h, we can multiply the given speeds by 1.852 to get the corresponding km/h values. So, for the first motion, the speed is 4 knots * 1.852 km/h = 7.408 km/h, and for the second motion, the speed is 5 knots * 1.852 km/h = 9.26 km/h.
Now, we can calculate the displacements for each segment of the boat's motion. Displacement is obtained by multiplying the speed by the time. So, for the first motion, the displacement is 7.408 km/h * 3 hours = 22.224 km, and for the second motion, the displacement is 9.26 km/h * 2 hours = 18.52 km.
Now, let's break down these displacements into x and y components by considering the directions. In the first motion, the boat is traveling 25 degrees East of North. We can split this displacement into its northward component (upwards) and eastward component (to the right). To calculate these components, we use trigonometry.
The northward component (y) can be found by multiplying the displacement by the sine of the angle. So, the northward displacement for the first motion is 22.224 km * sin(25) = 9.319 km.
The eastward component (x) can be found by multiplying the displacement by the cosine of the angle. So, the eastward displacement for the first motion is 22.224 km * cos(25) = 19.874 km.
For the second motion, the boat is traveling due South, so the displacement is entirely in the southward direction (downwards). Therefore, the y-component for the second motion is -18.52 km.
Now we have the x and y components for both motions. We can represent these components as vectors on a coordinate plane. The vector for the first motion can be represented as (19.874 km, 9.319 km), and the vector for the second motion is (0 km, -18.52 km).
To find the resultant vector, we need to add the individual vectors together. So, we add the x-components and the y-components separately.
For the x-component: 19.874 km + 0 km = 19.874 km.
For the y-component: 9.319 km + (-18.52 km) = -9.201 km.
Therefore, the resultant vector is (19.874 km, -9.201 km).
Note that the negative sign in the y-component indicates a southward direction.
I hope this helps! Let me know if you have any further questions.