Question 1085958: Two aircraft A and B are at the same height and are travelling horizontally at 500km/h. A is flying due north and B is flying due west. The bearing of B from A is 15 and the distance AB is 10km.
(i) Find the least distance between the aircraft in their subsequent motion.
(ii)the time, in seconds , for them to reach the position where they are the least distance apart.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two aircraft A and B are at the same height and are travelling horizontally at 500km/h.
A is flying due north and B is flying due west.
The bearing of B from A is 15 and the distance AB is 10km.
:
(i) Find the least distance between the aircraft in their subsequent motion.
They will be at their closest point when B is due north of A
Using the right triangle formed and using the law of sines, B will travel 2.588 km to be due north.
At 500 km/hr this would take about 18.6 seconds
Find the dist that A is from this point initially again using the law of sine, I got 9.66km.
During this 18.6 sec A will also travel 2.588 km, therefore
9.66 - 2.588 = 7.07 km least distance between A & B
:
(ii)the time, in seconds , for them to reach the position where they are the least distance apart. Calculated above 18.6 seconds
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