Relative velocities, and positions

  • Thread starter d=vt+1/2at^2
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In summary: To find the time when the separation between the ships is the least, one can either plot the distance between the ships over time or differentiate the function found in part b and set it equal to 0 to find the maximum or minimum point.
  • #1
d=vt+1/2at^2
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Homework Statement



-Ship A is located 4 km north and 2.5 km east of ship B
-ship A has a velocity of 22km/h south
-ship B has a velocity of 40km/h in a direction 37 degrees north of east

a) Find the velocity of A relative to B in unit vector notation, with i towards the east
b) Write an expression in terms of i and j for the position of A relative to B as a function of t, where t = 0 when the ships are in the positions described above
c)at what time is the separation between the ships least?
d) What is that least separation?


Homework Equations





The Attempt at a Solution



I believe the answer to part a, is V(A) = -22j

I have absolutely no idea how to do b, c, or d

Please do not solve the question for me, but if someone could point me in the right direction, it would be GREATLy appreciated!
 
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  • #2
a) you have to divide to vectors in different components, so for example the vector that describes the motion of A = (0i, -22j). You should do the same for B.

b) if you have the relative velocity we can assume that one of the ships doesn't move (which is the definition of 'relative motion'). so you begin with the initial distance between the ships and you this is becoming less by the second with the relative velocity.
 
  • #3
Ok, I got a and b, and now I am stuck on C. How do I find the time when the separation of the ships is the least?
 
  • #4
i don't know which formula you have fabricated at b. but if b is correct you can do two things to solve c.

1) you can plot it with on the y-axis the distance between the ships (delta x) and on the x-axis the time. this way you can see at what time the minimum occurs.

2) you can differentiate the function you found at b ( dx/dt). for the minimum let this equal to 0. since then you have a maximum or minimum found in your function. but i don't know if you are advanced enough to know this technique.
 
  • #5
My formula for B is correct, i tested it out on graph paper.

I got: -40cos37it - 46.1jt + 2.5i + 4j

To summarize, after one hour (since the velocities are in km/h), relative to ship B, ship A is (-40cos37+2.5) units West of ship B, and (-46.1+4) units south of ship B.
 
Last edited:

What is relative velocity?

Relative velocity is the velocity of an object in relation to another object. It is the difference in velocity between the two objects and is dependent on the frame of reference used.

How is relative velocity different from absolute velocity?

Absolute velocity is the velocity of an object in relation to a fixed point, such as the Earth. Relative velocity takes into account the motion of another object and is therefore dependent on the frame of reference used.

How do you calculate relative velocity?

To calculate relative velocity, you subtract the velocity of one object from the velocity of another object. The resulting velocity is the relative velocity between the two objects.

What is the formula for relative velocity?

The formula for relative velocity is: Vrel = V2 - V1, where Vrel is the relative velocity, V2 is the velocity of the second object, and V1 is the velocity of the first object.

How does relative position relate to relative velocity?

Relative position is the distance between two objects in relation to each other. Relative velocity takes into account the motion of these two objects, so the relative position will change as the relative velocity changes.

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