At noon, ship A was 14 nautical miles due north of ship B.  Ship A was sailing south at 14 knots (nautical miles per hour; a nautical mile is 2000 yards) and continued to  do so all day.  Ship B was sailing east at 7 knots and continued to do so all day.  The visibility was 5 nautical miles.  Did the ships ever sight each other?

Question
Asked Oct 18, 2019
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At noon, ship A was 14 nautical miles due north of ship B.  Ship A was sailing south at 14 knots (nautical miles per hour; a nautical mile is 2000 yards) and continued to  do so all day.  Ship B was sailing east at 7 knots and continued to do so all day.  The visibility was 5 nautical miles.  Did the ships ever sight each other?

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Expert Answer

Step 1

Let the two ships meet each other after time t. The diagrammatic representation of the given problem is shown below.

14
14(t
7t
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14 14(t 7t

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Step 2

The distance between them is evaluated as follows.

d =(14(r-1) (7)
= 196(t2+1-2t)+49r2
-196t249t2- 392t +196
245t2- 392t196
..1)
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d =(14(r-1) (7) = 196(t2+1-2t)+49r2 -196t249t2- 392t +196 245t2- 392t196 ..1)

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Step 3

...
(d2)=490 -392
dt
0 490t 392
392
490
t 0.8
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(d2)=490 -392 dt 0 490t 392 392 490 t 0.8

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Math

Calculus

Derivative