Calculus
posted by Becky on .
At 1:00 p.m. ship A is 25 km due north of ship B. If ship A is sailing west at a rate of 16km/h and ship B is sailing south at 20km/h, find the rate at which the distance between the two ships is changing at 1:30 p.m.

draw the triangle (lets W, S)
label the West leg W km, South leg Skm
Distance between ship x.
x= sqrt (W^2+S^2)
dx/dt= 1/2 *1/sqrt( ) * (2w *dw/dt + 2S ds/dt)
find dx/dt
Caculate S, W from 1/2 hr at given speeds.
you know dw/dt, ds/dt 
xa = 16 t
ya = 25
xb = 0
yb = 20 t
at 1/2 hour
xa = 8
ya = 25
xb = 0
yb = 10
z = distance between
z^2 = (xbxa)^2 + (ybya)^2
z^2 = (16 t)^2 + (20 t  25)^2
2z dz/dt = 2(16t)(16) + 2(20t25)(20)
z dz/dt = 256 t +400 t + 500
z dz/dt = 656 t + 500
now at 1/2 hour
z = sqrt(64 + 1225) = 35.9
so
35.9 dz/dt = 328+500
dz/dt = 23.1 km/hr 
THANKS FOR ALL THE HELP!
One question, how do you find xa,ya, xb, and yb? 
xa is the x position of the first ship
At time 0 it is at x = 0
then it proceeds in the west (negative x) direction at 16 km/hr
so the x position of A is (0  16 t) or just 16 t
Since it starts out 25 km north (positive y directio) and never goes north or sout, its Y position is always ya = 25
etc 
Oh i shoud've been more specific, what i meant to ask was how do you find xa, ya etc. at 1/2 hours?
Thanks in advance! :) 
OH NEVER MIND! I GOT IT HAHAHA!

Can you use that distance equation every problem or is it modified to fit this question?
Also, how did you find z at 1/2 hours? (z = sqrt(64 + 1225) = 35.9)?