Calculas: I can't figure out this problem?

Question

A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking?

I've been working on this problem for half an hour and can't figure it out. The answer is 837 divided by the square root of 8674. Can someone show me how to solve this problem step by step? It's greatly appreciated.

Answer 1

500^2+L^2 = Hyp^2
Differentiate above equation with respect to time,
2LL' = 2Hyp Hyp'
Hyp'
= LL'/Hyp
= 9300(9)/sqrt(500^2+9300^2)
= 837/sqrt(8674)
= 8.99 ft/s

Answer 2

Hehehe. You really should have paid more attention in that Geometry class ☺

Draw a picture (always a good place to start)
Notice that if you draw a line from the mans position tothe womans position, you have drawnthe hypotenuse of a large right triangle. One side of the triangle is 500 ft, and the other side is the combined distances of the mans north travel and the womans south travel. (You'll have to do a little bit of arithmetic to put numbers to those ☺) Now, remember that a right triangle with sides a and b and hypotenuse c satisfies
a² + b² = c²
and you're looking for dc/dt given a and db/dt. (and you know that db/dt is 9 ft/sec.)

You should be able to take it from here ☺

HTH

Doug

Answer 3

utilising the Sine Rule supplies sinC=25sin84/28 =0.8880 (4DP) giving C=sixty two.6° or 117.4° yet 117.4° isn't a threat in view that B=80 4° and angles of triangle won't be able to exceed a hundred and eighty°. So there is basically one triangle.