Please check.
I did these problems by drawing a graph ... So it would be great if you do it that way too if you need to correct me.
I know this is overwhelming but please take your time... It is easier for me to post all of these at once,since I can find it easier rather than posting many posts...
1. 11 units at 0 degree followed by 5 units along a bearing of 70 degrees
My answer: 13.6 units at 20.1 degrees
2. 8 units at 90 degrees followed by 6 units along a bearing of 210 degrees
My answer: 7.21 units at 136 degrees
3. 6 units at 270 degrees followed by 14 units along a bearing of 110 degrees
My answer: 8.61 units I DO NOT UNDERSTAND HOW TO FIND THE ANGLE BECAUSE WHEN I USED THE LAW OF COSINES I GOT 146 DEGREES...SO AM I SUPPOSED TO DO THIS??: 180-146= acute angle....BUT THEN I DON'T GET WHICH DIRECTION SHOULD I ADD UP THE ANGLE THAT SMOOCHES AT THE RESULTANT VECTOR... IN OTHER WORDS, WHEN STARTING ON THE Y AXIS OR THE NORTH POSITION DO I GO RIGHT OR LEFT AND WHY??????????
4. 4 units at 180 degrees followed by 9 units along a bearing of 320 degrees
My answer: 6.47 units at 243 degrees
5. A ship sails 50 mi on a bearing of 20 degrees and then 30 mi further on a bearing of 80 degrees . Find the resultant displacement vector as a distance and bearing.
My answer : 70 miles at 41.8 degrees
6. A plane flies 200 mi/hr along a bearing if 320 degrees. The air is moving with a speed of 60 mi/hr along a bearing of 190 degrees.
My answer: 168 mi/hr at 304 degrees
7. A scuba diver swims 100 ft/min along a bearing of 170 degrees. The water is moving with a current of 30 ft/min along a bearing of 115 degrees.
My answer: 116 ft/min at 156.5 degrees
8. Given: 120 yards at 80 degrees and 22 yards at 10 degrees
My answer: 129 yards at 70.8 degrees
first off, you move along a heading.
If you see something and determine its position, then the bearing is the direction from where you are.
Now on to the calculations.
#1. ok
#2. ok
#3. I do mine by converting each position to rectangular coordinates, then adding the vectors, then converting back to polar coordinates. Keeping in mind that a compass heading of x° is a polar angle of (90-x)°
So, for this one, I do
6@270° = -6,0
14 @ 110° = 13.16,-4.79
add them up to get 7.16,-4.79
d = 8.61
θ = -33.8
so, heading is 123.8
Using the law of cosines does get tricky.
#4. I get 6.47 at 296.6°
#5. I get 32.8 at 72.4°
#6. ok
#7. ok
#8. ok
Let's go through each problem one by one and correct any mistakes if necessary.
1. 11 units at 0 degrees followed by 5 units along a bearing of 70 degrees.
Your answer: 13.6 units at 20.1 degrees.
This seems correct. You can find the resultant displacement by using trigonometry to find the x and y components of each displacement and then adding them up.
2. 8 units at 90 degrees followed by 6 units along a bearing of 210 degrees.
Your answer: 7.21 units at 136 degrees.
This also seems correct. Again, you can find the x and y components of each displacement and then add them up.
3. 6 units at 270 degrees followed by 14 units along a bearing of 110 degrees.
Your answer: 8.61 units.
To find the angle between the two vectors, you can subtract the angles from 180 degrees. So in this case, 180 - 146 = 34 degrees.
To determine the direction of the resultant vector, you can start at the positive x-axis and rotate counterclockwise by the angle you calculated. So in this case, you would rotate counterclockwise by 34 degrees to get the direction of the resultant vector.
4. 4 units at 180 degrees followed by 9 units along a bearing of 320 degrees.
Your answer: 6.47 units at 243 degrees.
This seems correct. Same method as before, find the x and y components, and then combine them.
5. A ship sails 50 mi on a bearing of 20 degrees and then 30 mi further on a bearing of 80 degrees. Find the resultant displacement vector as a distance and bearing.
Your answer: 70 miles at 41.8 degrees.
This looks correct. You can again find the x and y components of each displacement, add them up, and then find the magnitude and direction of the resultant vector.
6. A plane flies 200 mi/hr along a bearing of 320 degrees. The air is moving with a speed of 60 mi/hr along a bearing of 190 degrees.
Your answer: 168 mi/hr at 304 degrees.
This seems correct. You can treat the plane's velocity and the air's velocity as vectors and find the vector sum.
7. A scuba diver swims 100 ft/min along a bearing of 170 degrees. The water is moving with a current of 30 ft/min along a bearing of 115 degrees.
Your answer: 116 ft/min at 156.5 degrees.
This looks correct. Same method as before, find the x and y components of each velocity, add them up, and then find the magnitude and direction of the resultant vector.
8. Given: 120 yards at 80 degrees and 22 yards at 10 degrees.
Your answer: 129 yards at 70.8 degrees.
This also seems correct. Again, find the x and y components of each displacement, add them up, and then find the magnitude and direction of the resultant vector.
Overall, your answers seem to be correct. Keep in mind to use trigonometry to find the x and y components of each vector, and then add them up to find the resultant vector.
To solve these problems using graphing methods, you'll need to use vector addition and trigonometry. Here is a step-by-step method to check your answers using graphs:
1. Start with a grid and draw a vector of 11 units in the positive x-direction (0 degrees). Then draw a second vector of 5 units at an angle of 70 degrees clockwise from the positive x-axis. Measure the magnitude and angle of the resultant vector.
2. Repeat the process for problem 2, drawing an 8 unit vector in the positive y-direction (90 degrees) and then a 6 unit vector at an angle of 210 degrees clockwise from the positive x-axis. Measure the resultant vector's magnitude and angle.
3. For problem 3, draw a 6 unit vector in the negative y-direction (270 degrees) and then a 14 unit vector at an angle of 110 degrees clockwise from the positive x-axis. Measure the magnitude and angle of the resultant vector.
When using the Law of Cosines, make sure you're using the correct angles in your calculations. The acute angle between the vectors should be used.
4. Repeat the process for problem 4. Draw a 4 unit vector in the negative x-direction (180 degrees) and then a 9 unit vector at an angle of 320 degrees clockwise from the positive x-axis. Measure the magnitude and angle of the resultant vector.
5. For problem 5, draw a 50-mile vector at an angle of 20 degrees clockwise from the positive x-axis. Then draw a second 30-mile vector at an angle of 80 degrees clockwise from the positive x-axis. Measure the magnitude and angle of the resultant vector.
6. Repeat the process for problem 6. Draw a 200 mph vector at an angle of 320 degrees clockwise from the positive x-axis. Then draw a second 60 mph vector at an angle of 190 degrees clockwise from the positive x-axis. Measure the magnitude and angle of the resultant vector.
7. For problem 7, draw a 100 ft/min vector at an angle of 170 degrees clockwise from the positive x-axis. Then draw a second 30 ft/min vector at an angle of 115 degrees clockwise from the positive x-axis. Measure the magnitude and angle of the resultant vector.
8. Repeat the process for problem 8. Draw a 120-yard vector at an angle of 80 degrees clockwise from the positive x-axis. Then draw a second 22-yard vector at an angle of 10 degrees clockwise from the positive x-axis. Measure the magnitude and angle of the resultant vector.
By comparing the magnitudes and angles you measured on the graph to your calculated answers, you can check if your solutions are correct. If they match, then your answers are likely correct. If they don't match, double-check your calculations and angles to find the error.