Posted by agora on Thursday, May 2, 2013 at 5:41am.
Ship A is sailing due south at 25 km/hr. At the same time, a second ship B, 50km miles south of A, is sailing due east at 20 km/hr.
(a) at what rate are they approaching or separating at the end of one hour?
(b) At what rate are they approaching or separating at the end of two hours?
(c) When do they cease to approach each other and how far apart are they at that instant

calculus  Steve, Thursday, May 2, 2013 at 11:37am
Let B start at (0,0). Then the positions of the boats at time t are
A(t) = (0,5025t)
B(t) = (20t,0)
and the distance d is thus
d^2 = (20t)^2 + (5025t)^2
= 1025t^2  2500t + 2500
2d dd/dt = 2050t  2500
At t=1, d ~= 32
64 dd/dt = 20502500
dd/dt = 7.03 km/hr
At t=2, d = 40
80 dd/dt = 41002500
dd/dt = +20
dd/dt=0 when t=1.22 so d = 31.23
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