Question about 2 ships - vectors?

In summary: But boat A is traveling 20° west of north, so it's velocity has a component that is to the left. So boat B would have to subtract that component from boat A's velocity to get the speed it sees. So that's what you need to do.In summary, the two ships, A and B, leave port together and travel for two hours. Ship A travels at 35 mph in a direction 20° west of north, while ship B travels 10° east of north at 40 mph. Using the law of cosines, the distance between the two ships after two hours is approximately 93.32 miles. To calculate the speed of ship A as seen by ship B, we need to
  • #1
Star Forger
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Homework Statement



Ships A and B leave port together. For the next two hours, ship A travels at 35 mph in a direction 20° west of north while the ship B travels 10° east of north at 40 mph.

(a) What is the distance between the two ships two hours after they depart (in miles)?


(b) What is the speed of ship A as seen by ship B (in mph)?


Homework Equations





The Attempt at a Solution



I have no idea how to approach this problem. I believe it is vectors, however as I said I'm not sure. Any help would be greatly appreciated.
 
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  • #2
Start by drawing 2 vectors from one point, let's say (0,0)
-One vector will go at a 20° angle to the west (of north) and the other will go 10° east (of north)
-Since it's 2 hours you can make the vector length double (70 and 80).
-You will end up have 1 angle, 2 sides
-You can now use the law of cosines to solveI believe this is correct, if not someone will correct me :p

Edit: that's part A.
 
  • #3
Thank you, that made a lot of sense and I calculated part A correct. How would I calculate part B though? What does speed as seen by the other mean?
 
  • #4
Pretend you were standing on boat B watching boat A. If both boats were traveling in tje same direction at the same speed, boat A would appear stationary to someone on boat B.
 
  • #5


I can provide a response to this question using mathematical and scientific principles. First, let's define some variables to help us solve the problem.

Let d be the distance between the two ships after two hours, vA be the speed of ship A, and vB be the speed of ship B.

(a) To find the distance between the two ships after two hours, we can use the formula for distance: d = vt, where v is the speed and t is the time. We know that ship A travels at 35 mph for 2 hours, so dA = 35*2 = 70 miles. Similarly, ship B travels at 40 mph for 2 hours, so dB = 40*2 = 80 miles. To find the distance between the two ships, we can use the Pythagorean theorem: d = √(dA^2 + dB^2) = √(70^2 + 80^2) = √(4900 + 6400) = √11300 ≈ 106.3 miles.

(b) To find the speed of ship A as seen by ship B, we can use the concept of relative velocity. Since ship B is traveling at 40 mph, it can be thought of as a frame of reference moving at 40 mph. This means that the velocity of ship A as seen by ship B will be the sum of its actual velocity and the velocity of the frame of reference (ship B). We can use the formula vA' = vA - vB to find the velocity of ship A as seen by ship B: vA' = 35 - 40 = -5 mph. This negative sign indicates that ship A appears to be moving in the opposite direction as seen by ship B. However, to find the speed, we need to take the magnitude of this velocity, which is 5 mph. So, ship A appears to be moving at a speed of 5 mph as seen by ship B.

In conclusion, the distance between the two ships after two hours is approximately 106.3 miles, and the speed of ship A as seen by ship B is 5 mph.
 

FAQ: Question about 2 ships - vectors?

1. What are vectors and how are they used in relation to 2 ships?

Vectors are mathematical quantities that have both magnitude and direction. In relation to 2 ships, vectors can be used to represent the movement and position of each ship. They can also be used to calculate the distance between the two ships and their relative velocities.

2. How do you calculate the velocity of 2 ships using vectors?

To calculate the velocity of 2 ships using vectors, you will need to first determine their positions and respective velocities. Then, you can use the vector addition formula to find the combined velocity of the 2 ships. This will give you a vector with both magnitude and direction, representing the overall velocity of the 2 ships.

3. Can vectors be used to predict collisions between 2 ships?

Yes, vectors can be used to predict collisions between 2 ships. By using the velocity vectors of each ship, you can determine if their paths will intersect at any point in time. This can help predict and prevent potential collisions.

4. How do you use vectors to determine the shortest distance between 2 ships?

To determine the shortest distance between 2 ships using vectors, you will first need to find the vector that connects the two ships. Then, you can use the dot product formula to calculate the perpendicular distance between the two ships. This will give you the shortest distance between them.

5. Are there any limitations to using vectors in analyzing 2 ship movements?

While vectors can provide valuable information about the movements of 2 ships, they do have some limitations. For instance, they do not take into account external factors such as wind or currents that may affect the ships' movements. Additionally, vectors may not accurately represent the complex movements of ships in real-life situations. Therefore, other methods and technologies may also need to be used in conjunction with vectors for a more comprehensive analysis of 2 ship movements.

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