SOLUTION: 5. The position of a lost hiker, H, is given by the parametric equations {{{x= 4 - 3t}}} {{{y= 3 - 2t}}} , where position is measured in km, and time in hours. The position

Question 389493: 5. The position of a lost hiker, H, is given by the parametric equations

, where position is measured in km, and time in hours. The position of his rescue party, R, is given by

.
a) Find the initial position of the hiker and his rescue party.
b) Find the velocity vector of each.
c) When is the rescue party closest to the hiker and how close are they at this time?

C is giving me the most trouble,

any help is appreciated ^.^
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
(a)
Set
(4,3) and (3,-5)
(b)
For velocity vectors:
hiker:
at 180 degrees + arc tan(2/3)
at degrees
rescue party:
at 180 degrees - arc tan(4)
at degrees
(c)
I need a general formula for the distance between them
It would be square root of(x2 - x1)^2 + (y2 - y1)^2)

The 1st term is zero when , then the distance
would be
The 2nd term is zero when
Then distance =
I think they come the closest in 1 hr 20 min and
they are 1.67 km apart.
This is kind of a guess, I would get another opinion, too
RELATED QUESTIONS
Hello I hope someone can help me. Here is the question: THe position of an object moving (answered by jim_thompson5910)

The position function of a particle in rectilinear motion is given by s(t) = 2t^3 + 21t^2 (answered by Boreal,ikleyn)

The position of an object moving in a straight line is given by s=2t^2-3t, where s is in... (answered by Fombitz)

A particle is moving according to an equation of motion. Its position after t seconds is... (answered by ikleyn)

Consider the curve given by the parametric equations: x = 3t^2 - 6t y = t^4 - 2t^3 -... (answered by robertb)

The position of a 140kg body is given by S = 3t^2 - 7t + 4. Where S is in meters and t is (answered by Fombitz)

The position of an object moing in a straight line is given by s=2t^2-3t, where s is in... (answered by Earlsdon)

In a certain region, the electric potential due to a charge distribution is given by the... (answered by ikleyn)

The position of a particle is given as s(t) = 2/5t^5 −2t^4 + 2t^3 where t is in hours... (answered by Boreal)