1. relative velocity

a ship A has position -8i+4j km relative to a small island O. another ship B has position 24i-12j km relative to O. the velocities of a and b respectively are 3i+j km/h and i+2j km/h show they are on a collision course.

usually i take away there velocities but i dont know what to do when i am given positions.

2. Re: relative velocity

You can start by developing expressions for the x and y coordinates of ships A and B as a function of time. Ship A's velocity component in the x-direction is 3, and ship B's velocity component in the x-direction is 1. Hence as a function of time the x-coordinates of the two ships are:

x_A = -8 + 3t
x_B = 24 + t

Set these equal and solve for t, and you get t = 16. hence at that time both ships share the same x coordinate.

Next see if at t=16 you have y_A = y_B; if so, then at that time both ships A and B have the same x and y-coordinates, so they are ay the same point at the same time.

3. Re: relative velocity

The position of ship A at time t hours after the time positions are given is -8i+ 4j+ (3i+ j)t= (3t- 8)i+ (t+ 4)j.
The position of ship B at time t hours after the time positions are given is 24i- 12j+ (i+ 2j)t= (t+ 24)i+ (2t- 12)j.

The two ships will "collide" if the two ships are at the same place at the same time. That is, they will collide if and only if there exist a value of t satisfying (3t- 8)i+ (t+ 4)j= (t+ 24)i+ (2t- 12)j so satisfying both 3t- 8= t+ 24 and t+ 4= 2t- 12.

(Normally, of course, we can not find one value that satisfies two equations. Normally, boats don't collide!)

4. Re: relative velocity

How dold you show that they are on a collision course

5. Re: relative velocity

Originally Posted by markosheehan
How dold you show that they are on a collision course
by showing they arrive at the same position $(x(t),y(t))$ at the same time ...

ChipB showed they would be at the same x-position at t = 16

Are they at the same y-position at t = 16?

6. Re: relative velocity

Is there some way where you take away there velocities and then if the job components cancel out it must mean they are on a collision course can you do that here

7. Re: relative velocity

WTH is a "job component" ?

J. component

9. Re: relative velocity

in their answers they assumed they were going to collide . all i needed to show was that they were on a collission course. i know how to show this know you get velocity of a relative to b which is 2i-j and you get there relative displacement which is -32i +16j . now if you get the slope of relative velocity and direction. or the angle. i will get the slope. -1/2 and -1/2 therefore they will collide. sorry for spelling.