SOLUTION: can anyone help with the following assignment question, Two aircrafts take off simultaneously from different airports. As they climb, their positions relative to an air traffic

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Question 168322: can anyone help with the following assignment question,
Two aircrafts take off simultaneously from different airports. As they climb, their positions relative to an air traffic control centre t minutes later are given by the vectors:
r1 = 4i-30j +t(8i+2j+0.3k)
r2 = 12i+26j+ t(6i-3j+0.8k)
where i direction is due east, the j is due north and k is vertical distance and the units are kilometres.
a) find the coordinates of the point over the groun where the two planes cross
b) find also the difference in height and time that they both pass this point.
this is a completely different question to the examples we have done in the handouts and lessons so i am really struggling with this.
kevin
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
OK, let's break down the positions of each.
r1+=+4i-30j+%2Bt%288i%2B2j%2B0.3k%29
r1=4i-30j%2B8ti%2B2tj%2B0.3tk
r1=%284%2B8t%29i%2B%28-30%2B2t%29j%2B0.3tk
and similarly,
r2+=+12i%2B26j%2B+t%286i-3j%2B0.8k%29
r2=12i%2B26j%2B6ti-3tj%2B0.8tk
r2=%2812%2B6t%29i%2B%2826-3t%29j%2B0.8tk
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Now you have the position of both planes as a function of t.
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When the planes cross, their i and j coordinates will be the same.
r1%5Bi%5D=r2%5Bi%5D
4%2B8t=12%2B6t
2t=8
t=4
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r1%5Bj%5D=r2%5Bj%5D
-30%2B2t=26-3t
5t=56
t=56%2F5
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There is a problem.
For them to pass the same i,j point, the times need to match.
When t=4,
r1x=r2x=36
r1y=-30%2B2t=-30%2B8=-22
and similarly,
r2y=26-3t=26-12=14
As you can see the x coordinates match, the y-coordinates don't.
The same thing happens at t=56/5.
There is no point in time when "i" positions and "j" positions match for the planes.
Please re-check the numbers and re-post.