Am I working this problem correctly?
Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots(nautical miles per hour) and the other is headed directly south at a constand speed of 22 knots. Express the distance d between the boats as a funtion of the time t.
(35,0)(0,22)
f(t)=sqrt(35^2 + 22^2)
=sqrt(1709)
=41.34
Is that right?
No, this function gives you the distance between the two ships with respect to the elapsed time. So after
1 hour ---> d = 41.34 nmi
2 hours ---> d = 82.68 nmi
3 hours ---> d = 124.02 nmi
and so on.
If you want to calculate t you have to solve the equation of the function for t.
It's the expression you've been talking about over and over. You think of the two boats as moving along the legs of a right triangle and the distance between them is the hypotenuse of that triangle. earboth calculated the general length of this hypotenuse, based of time which is what you want. If you don't get the answer then you don't fully understand the question I think, which is fine. Just ask us to clarify something.
I understand that part. What was confusing me was the pythagorean theorem and the distance formula. That and yes, I do not fully understand it. It's the only question that has been irking me for the past 2 days! I could just as easily miss the question, but I'm not that type of person. I'd like to understand it since I still have about 6 weeks left of class.
Well I'm glad you're the type to make sure you get them all! You'll fit in here well. You understood the basic idea of how to use the right triangle formed by the boats to solve for the distance, you just forgot to show how the triangle will change with time, which is what earboth added. I think you see from earboth's post the reasoning. The distance formula is really just the pythagorean theorem in disguise, which makes it one less thing to memorize if you think of it that way.