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.
The answer they get is 60.5 degrees north or 29.5 degrees north of east, but they show no work, just the answer. When I draw out the vectors, what do I use to determine the length of each vector? The hours? The knots? What scale 1mm = 1hour, or 1mm = 1knot?
Steve was nice enough to give me a hand, but me not being the smartest one on the block is still a little confused. Thank you Steve, very much appreciated!!! This site is the best.
Math books drive me crazy with their misuse of navigational language. You travel on a heading as used in the second sentence. A bearing is what direction you look to see something. (The enemy is on a bearing of 185 degrees true.)
Anyway start at (x,y) = (0,0)
It is heading 25 deg east of north
in x-y coordinates that is 25 degrees clockwise from the Y axis so we would say
X velocity = 4 sin 25 = 1.69 knots
Y velocity = 4 cos 25 = 3.625 knots
after three hours x = 3*1.69 = 5.07 nautical miles
and y = 3*3.625 = 10.875 nautical miles
Now we turn south (negative y axis)
go south for two hours at 5 knots = 10 nautical miles
so in the end after 5 hours
x position = 5.07 naut miles
y position = 10.875-10 = .875 naut miles
so that position on you x-y graph is
(5.07, .875 )
tan angle up from x axis = y/x =.875/5.07
so angle up from x = 9.79 degrees
so angle clockwise from north = 90-9.79 = 80.2 degrees east of north.
If you want it in km rather than nautical miles, multiply all distances by 1.852
Sorry the answer they have is 60.5 degrees east of of north or 29.5 degrees north of east. There would be two vectors right, so do you take the degrees from the resultant? Thanks Damon, I do not nothing about this stuff at all. The question says my answer should be found by drawing, so it may not match.
I gave the wrong answer at first. Sorry.
Thanks Damon, figured it all out thanks to your people's help, you rock. Thanks buddy!!!
No problem at all! I'm here to help. Let's break down the problem step by step so you can understand how to approach it.
First, we need to determine the magnitude and direction of each vector. The magnitude represents the length of the vector, and the direction is the angle at which the vector is pointing.
Let's start with the first part of the problem: the boat traveling on a bearing of 25 degrees East of North at a speed of 4 knots for 3 hours.
To determine the magnitude of the vector, we need to calculate the distance traveled by the boat. Since the speed is given in knots and the time is given in hours, we can use the formula:
Distance = Speed x Time
In this case, the speed is 4 knots and the time is 3 hours, so the distance traveled is 4 knots x 3 hours = 12 nautical miles (nautical miles are the same as knots).
Now, let's determine the direction. The boat is traveling on a bearing of 25 degrees East of North, which means it's 25 degrees to the right (or east) of north. We can represent this as an angle measured clockwise from the north direction.
Now, let's move on to the second part of the problem: the boat changing its heading to due South and traveling at a speed of 5 knots for 2 hours.
Using the same formula as before, we can determine the distance traveled:
Distance = Speed x Time
Distance = 5 knots x 2 hours = 10 nautical miles
The direction is due South, which means the boat is pointing directly downwards.
Now that we have determined the magnitude and direction of each vector, we can draw them on a vector diagram. However, in order to draw them accurately, we need to establish a scale.
For example, you can use a scale where 1 cm on the diagram represents 1 knot or 1 hour. This scale allows you to accurately represent the magnitude of each vector.
Once you have drawn the vectors accurately, you can use vector addition to find the resultant vector. To do this, you simply place the tail of the second vector at the head of the first vector and draw a line connecting the tail of the first vector to the head of the second vector. The resultant vector is the line that goes from the tail of the first vector to the head of the second vector.
After finding the resultant vector, you can measure its angle and magnitude using a protractor and ruler, respectively.
I hope this helps you understand how to approach the problem and draw the vectors accurately. If you have any further questions, feel free to ask!