Question

At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing north at 25km/h. How fast is the distance between the ships changing at 4:00 p.m.

If you could explain how I should do this, that would be great PLEASE!!!

Answer 1

I think the distance between ship A and ship B at 4 pm is 260 km.

Answer 2

I forgot to add that the correct answer is \[\approx\]55.4 km/h

Answer 3

You need to find an instantaneous rate of change. The first step is to find your function. Consider points in the cartesian plane where A is at (0,0) and B is at (100,0). The position of A now at a given time t (where time is hours and t=0 represents noon) can be found now by (0, -35t) and, likewise for B by (100, 25t).

What we care about is the distance though so we can plug these functions into the distance function d(x,y) = sqrt( (x1-x2)^2 + (y1-y2)^2 ) and get the function

f(t) = sqrt(100^2 + 60^2*t^2)

To find the rate of change, we need the derivative,

f'(t) = 180t/sqrt(9t^2+25)

and, indeed, f'(4) is approx. 55.4

Answer 4

eh... my distance function should actually be d((x1,y1), (x2,y2))=... lazy habits die hard.