calculus
posted by Anonymous .
Could someone help me et up this problem?
Two people start from the same point. one walks east at 3mi/h and the other walks northeast at 2mi/h. How fast is the distance between the poeple changing after 15 minutes?
I think this is what I would do:::
First I would set up a triangle:
hypotenuse=h (northeast walking person)
height=y
leg=x (north walking person)
GIVEN: dx/dt=3mi/h
dh/dt=2mi/h
Need to find dy/dt when t=15.

East problem
East walker at 3 mi/hr
NE walker at 2 cos 45 mi/hr
East distance between = (3 1.41)t = 1.59 t
North distance between = 1.41 t
h = hypotenuse = t sqrt(1.59^2 + 1.41^2)
= 2.13 t
now find dh/dt
dh/dt = 2.13 mi/hr 
your work doesn't match the wording of the question.
Where does it mention a northwalking person? (your x)
There isn't even a right angled triangle
I drew a horizontal line to the east (to the right)
then from the same starting point a line at 45º to the other one (going northeast)
(make the horizontal a little longer, it represents 3 mph)
let the distance between their endpoints be x
let the time after they both leave be t hours.
then the 'goingeast' line has length 3t
the 'northeast' line is 2t
by Cosine Law
x^2 = (3t)^2 + (2t)^2  2(3t)(2t)cos 45º
= 13t^2  12t^2cos45
= 13t^2  6√2 t^2
dx/dt = 26t  12√2t
when t = 15 min = 1/4 hour
dx/dt = 26(1/4)  12√2(1/4)
= 2.26 mph 
thanx I thought I had to use the cosine law but I wasn't quite sure how to.
But how did you decide that the angle would be 45 degrees? 
where does a direction of NorthEast go in relation to East ?
What is the angle between North and East?
Respond to this Question
Similar Questions

Related rates
Two people start from the same point. One walks east at 1 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes? 
calculus
Two people start from the same point. One walks east at 3 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes? 
calculus
Two cars start from the same point at the same time. One travels north at 25 mph, and the other travels east at 60 mph. How fast is the distance between them increasing at the end of 1 hr? 
Calculus
Two people start from rest at the same point. One walks east at 3 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changingg after 15 minutes? 
Calculus
Two people start from the same point. One walks east at 5 mi/h and the other walks northeast at 7 mi/h. How fast is the distance between the people changing after 15 minutes? 
Calculus
Two lovers have a spat and swear they will never see each other again. The girl walks due south at 6 mph while the boy walks at 10 mph on a heading of North 60 degrees West. How fast is the distance between them changing 30 minutes … 
Calculus
Two lovers have a spat and swear they will never see each other again. The girl walks due south at 6 mph while the boy walks at 10 mph on a heading of North 60 degrees West. How fast is the distance between them changing 30 minutes … 
math
Two people start from the same point. One walks east at 4 mi/h and the other walks northeast at 3 mi/h. How fast is the distance between the people changing after 15 minutes? 
math
tow people begin walking from the same point at the same time. One walks due south at 3 mph and the other walks southeast at 4 mph. Approximately how far apart are the two after one hour walking? 
math
Two people start at the same point One walks east at 2mph and the other walks southwest at 3mph. How fast is the distance between them changing after 30 minutes?