How Do Ships A and B Move Relative to Each Other?

In summary, the ships will be 110 nautical miles apart after 2 hours and bearing B will be 82.548 degrees west of south.
  • #1
Dante Tufano
34
0
Two ships, A and B, leave port at the same time. Ship A travels northwest at 19 knots and ship B travels at 28 knots in a direction 40° west of south. (1 knot = 1 nautical mile per hour; see Appendix D.)
(a) What is the magnitude the velocity of ship A relative to B?
35.181 knots

(b) What is the direction of the velocity of ship A relative to B?
_____ ° east of north

(c) After what time will the ships be 110 nautical miles apart?
_____ h

(d) What will be the bearing of B (the direction of B's position) relative to A at that time?
_____° west of south


2. Vab = Vas - Vbs
Vas = -19cos45 + 19sin45 = -13.435i + 13.435j
Vbs = -28cos50 - 28sin50 = -17.998i - 21.449j
Vab = 4.563i + 34.884j
magnitude of Vab = 35.181
arctan(34.884/4.563) = 82.548 degrees

3. For some reason, this value for the angle (which I'm trying to find for part b) is wrong. Any ideas on what I did wrong guys?
 
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  • #2
Some help anybody? Please
 
  • #3
It looks like the problem wants the angle measured East of North. The arctangent function is giving you the angle measured from the horizontal axis (i.e. East).

So, what do you need to do to find the angle as measured from the vertical axis?
 
  • #4
Dante Tufano said:
arctan(34.884/4.563) = 82.548 degrees
I didn't confirm your arithmetic, but you need to express your answer as requested: Degrees east of north.
 
  • #5
Oh, right! Thanks a lot guys, I'll try that out.

Edit: It worked! I subtracted the angle from 90 degrees and it was the correct answer
 
Last edited:
  • #6
Now how do I solve part D? I tried adding 180 degrees to the value of the angle for part B, but apparently that's wrong. Any advice?
 
  • #7
Dante Tufano said:
Now how do I solve part D? I tried adding 180 degrees to the value of the angle for part B, but apparently that's wrong. Any advice?
Why add 180 degrees to the answer for part B? It's perfectly OK to swing the velocity vector by 180 degrees, which is probably what you were thinking. Draw a diagram showing their relative positions, then read off the answer.

Once again, be sure to express your answer as requested: Degrees west of south.
 

Related to How Do Ships A and B Move Relative to Each Other?

1. What is relative motion of ships?

Relative motion of ships refers to the movement of two or more ships in relation to one another. It takes into account the position, direction, and speed of each ship to determine their relative positions and movements.

2. How is relative motion of ships calculated?

The relative motion of ships can be calculated using vector addition. Each ship's velocity (speed and direction) is represented as a vector, and the vectors are added together to determine the overall relative velocity between the ships.

3. What factors affect relative motion of ships?

The relative motion of ships can be affected by various factors such as wind, ocean currents, and the size and shape of the ships. Additionally, the relative motion may also be affected by the ships' maneuvering and the angle at which they approach each other.

4. Why is understanding relative motion of ships important?

Understanding relative motion of ships is important for navigation and collision avoidance. It allows ships to anticipate the movements of other vessels and make necessary adjustments to avoid collisions.

5. How does relative motion of ships differ from absolute motion?

Relative motion of ships takes into account the movement of one ship in relation to another, whereas absolute motion refers to the movement of a ship in relation to a fixed point, such as the Earth's surface. Absolute motion is typically used for navigation purposes, while relative motion is more important for collision avoidance.

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