# Calculus

At noon of a certain day,ship A is 60 km due north of ship B. If A sails east at 12 km/hr and B sails north 9 km/hr,determine how rapidly the distance between them is changing 2 hrs later. Is it increasing or decreasing?

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1. If we call A's position at noon (0,0) then we have the positions of A and B after t hours

A: (12t,0)
B: (0,60-9t)

The distance is thus

d^2 = (60-9t)^2 + (12t)^2 = 225t^2-1080t+3600
At t=2, d=√(42^2+24^2)=√2340=48.37

So, at any time t,

2d dd/dt = 450t-1080

Now just plug in your values

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posted by Steve
2. 2d dd/dt = 450t-1080
dd/dt = 900-1080/(2*48.37)=-1.86

this is what I get when I substitute the values.Is it correct?

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posted by 123

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