Question

Problem: Two particles are moving in the xy-plane. The move along straight lines at constant speed. At time t, particle A's position is given by x=t+2, y=1/2t-3 and particle B's position is given by x=12-2t, y=6-1/3t.
(a) Find the equation of the line along which particle A moves.
(b) Find the equation of the line along which particle B moves.
(c) Find the time (value of t) at which the distance between A and B is minimal.

NEED HELP PLEASE.. :)

Answer 1

Okay, so when they say "Fine the equation of the line" I think it to mean they want you to find \(y = f(x)\). If that is the case then my solution would be:
1) Solve for t in terms of x. \(t = f(x)\)
2) Plug it into y. \(y = g(t), f(x) =g(t(x))\).

Answer 2

those parametric equations don't describe straight lines...

Answer 3

For (c) they seem to want you to find the minimum euclidean distance. So I would just plug the equations into the distance formula and use the calculus you learned for minimization (find critical numbers, etc).\[
d(t) = \sqrt{[x_1(t) - x_2(t)]^2+[y_1(t) - y_2(t)]^2}
\]

Answer 4

@dpaInc Yeah I was wondering about that too.... maybe they meant curves?

Answer 5

possibly...

Answer 6

the equation of the line along which A moves y=(1/2)x-5
the equation of the line along which B moves y=(1/6)x+12
the time at which the distance is minimal happens when both particles are at (-36,6)