Solve Calculus Problem: Man & Woman Moving Apart

[Triggy]

Homework Statement

Hello everyone. I'm studying engineering and I'm doing calculus this year and next year as part of my degree. We get problem sheets with lots of exercises to do as practice. I'm using the James Stewart Calculus and Concepts textbook.

Anyway, I got stuck on the following question in my problem sheet.

A man starts walking north at 1.2m/s from a Point P. Five minutes later a woman starts walking south at 1.6m/s from a point 200m due east of P. At what rate are the people moving apart 15min after the woman starts walking?

Homework Equations

The Attempt at a Solution

So I drew point P on a piece of paper. The rate at which the two people are moving apart is their velocity right? their distance with respect to time. So if I let S(t) equal 1.2t + 1.6t + (dist he has traveled after 5 minutes) + (distance between them at the start) I would get S(t) = (1.2t + 1.6t + 360) + 200.

I must be missing something because then the derivative will be a constant...

 

[trajan22]

Pay attention to the direction they are traveling in, and where their start points are. The woman does not travel due south from the mans initial point she is east of him. If you draw this out you should see that the distance between them after time t is not just a vertical line.

 

[Triggy]

Yes I know, if you draw them out you get a diagonal line between them. I did take that into account by adding in the 200m between them. So is my formula correct?

 

[AKG]

Let P be the origin, let the positive y-axis point north and the positive x-axis point east. Find the man's position at time t, (x_M(t),y_M(t)) in terms of t, as well as the woman's position at time t, (x_W(t),y_W(t)), and use the Pythagorean theorem to express the distance between the two people as a function of t.

 

[NateTG]

BTW, this problem is quite easy to do without calculus.