Ship a is 32 miles north of ship b and is sailing due south at 16 mph. ship b is sailing due east at 12 mph. at what rate is the distance between the ships changing an hour later? are they getting closer together or farther apart?

-5.6 mi/h

Explanation:

= Velocity of ship A = -16 mi/h (negative as the distance is decreasing)

Distance ship A travels in 1 hour = 16×1 = 16 mi

a = Distance remaining = 32-16 = 16 mi

= Velocity of ship B = 12 mi/h

b = Distance ship B travels in 1 hour = 18×1 = 12 mi

c = Distance between A and B after 1 hour = √(a²+b²) = √(16²+12²) = 20 mi

From Pythagoras theorem

a²+b² = c²

Now, differentiating with respect to time

∴ Rate at which distance between the ships is decreasing one hour later is 5.6 mi/h

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