I think you need to find out when the hypotenuse changes from minimizing the distance as t moves west and s moves south to when the hypotenuse starts increasing the distance and then find that distance of the hypotenuse at that moment.
Hey, I have this problem that I am halfway done, but I do not know how to solve the second portion.
Question
Ship S is 41 Km due North of ship T. Ship S sails south at a rate of 9 km/h. Ship T sails west at 10 km/h.
a) At what rate are they approaching or separating one hour later?
b) When do they cease to approach one another and how far apart are they at this time?
Solution
a)
I figured out the distance after 1 hour: 33.52km
I then figured out the rate of change of the seperation/approach: 0.57kmh (approaching)
b) I do not know how to solve this part though. I could use the equation I used to find the rate of change, but setting that to zero really doesn't help in finding 3 other variables. Help?
I haven't done related rates in awhile but when you are minimizing or maximizing you need two equations. One will be since we want to minimize c. The other might be the area of triangle not 100% on that though.
What we know:
From this, I think you will have to implicit differentiate the Pythagorean identity but after that I am a little hazy on what needs to be done.
Yes it does - at least, you don't need to worry about hypotenuse z because it goes to zero with dz/dt (if it's on the dz/dt side of the equals sign) or else is merely the denominator of a zero-valued fraction (if it's on that side). And you know that for y you can substitute 41 - 9/10 x.