Homework Help: calculus

Posted by Anonymous on Monday, March 30, 2009 at 12:20pm.

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.

calculus - Damon, Monday, March 30, 2009 at 12:39pm
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
calculus - Reiny, Monday, March 30, 2009 at 12:47pm
your work doesn't match the wording of the question.
Where does it mention a north-walking 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 north-east)
(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 'going-east' line has length 3t
the 'north-east' 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
calculus - Anonymous, Monday, March 30, 2009 at 12:52pm
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?
calculus - Reiny, Monday, March 30, 2009 at 12:55pm
where does a direction of North-East go in relation to East ?
What is the angle between North and East?

Answer this Question

Related Questions

calculus - Two people start from the same point. One walks east at 3 mi/h and ...
Calculus - Two people start from rest at the same point. One walks east at 3 mi/...
Related rates - Two people start from the same point. One walks east at 1 mi/h ...
Math - A man walks one mile east, then he walks one mile northeast and then he ...
physics - a woman walks 2 km due east and then walks 4 km in the direction 30 ...
maths - a hiker walk due east at 4km per hour and a second hiker starting from ...
physics - A person walks 37.0◦ north of east for 5.00 km. Another ...
english - Break the shoes in thoroughly on short walks before going on an ...
Math - John walks 20km due east then turns 270 degrees anticlockwise and walks ...
physics - A man walks 3 miles east in 1 hour at a constant velocity, then walks ...

For Further Reading

First Name:
School Subject:
Answer: