Relative Velocity and Position of Ships A and B: Solving for Least Separation

Click For Summary
SUMMARY

The discussion focuses on calculating the relative velocity and position of two ships, A and B, with specific coordinates and velocities. Ship A is positioned 3.3 km north and 2.7 km east of Ship B, moving south at 22 km/h, while Ship B moves at 40 km/h at an angle of 37° north of east. The relative velocity of Ship A to Ship B is determined to be -31.95i - 46.07j. The participants discuss expressing the position of Ship A relative to Ship B as a function of time and finding the time of least separation between the ships.

PREREQUISITES
  • Understanding of vector mathematics and components (i.e., i and j notation)
  • Familiarity with relative velocity concepts
  • Knowledge of trigonometry, specifically angle conversions and sine/cosine functions
  • Ability to solve quadratic equations for time and distance calculations
NEXT STEPS
  • Learn how to express vectors in component form using i and j notation
  • Study the principles of relative motion in physics
  • Explore methods for minimizing distance between moving objects
  • Investigate the application of calculus in optimizing functions for least separation
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and vector analysis, as well as educators looking for practical examples of relative motion problems.

Dante Tufano
Messages
32
Reaction score
0
Ship A is located 3.3 km north and 2.7 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37° north of east.

(a) What is the velocity of A relative to B?

(b) Write an expression for the position of A relative to B as a function of t, where t = 0 when the ships are in the positions described as above.

(c) At what time is the separation between the ships least?

(d) What is that least separation?


2. Homework Equations : Vaw = Vab + Vbw

3. Okay, so I got the answer for part a, which is -31.95i - 46.07j, but I'm completely lost on the rest of the parts. I have no idea on how to express b in terms of i and j, let alone solve for it, any ideas?
 
Physics news on Phys.org
Okay, so I figured out part b, but how can I go about doing part c?
 

Similar threads

Relative velocity passing a ball between two soccer players
  • · Replies 5 ·
Replies
5
Views
3K
To find the closest approach of two ships
  • · Replies 2 ·
Replies
2
Views
3K
Relative velocity ship problem intuitively
  • · Replies 3 ·
Replies
3
Views
3K
How would i find the velocity of the ship relative to earth?
  • · Replies 2 ·
Replies
2
Views
4K
Relative Velocity of Two Ships: When Is Their Separation Least?
  • · Replies 5 ·
Replies
5
Views
10K
Will Two Ships Collide Based on Different Methods?
  • · Replies 6 ·
Replies
6
Views
2K
Relative velocities, and positions
  • · Replies 4 ·
Replies
4
Views
7K
Launch service between two stations along a flowing river
  • · Replies 21 ·
Replies
21
Views
1K
To find the time for which a vessel is within range of these guns
  • · Replies 4 ·
Replies
4
Views
1K
Relative motion in two dimensions question
  • · Replies 4 ·
Replies
4
Views
5K