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.