15 years ago
b1r2a0n5g1e9l9l0

Help with Parametric Equations?

Just a technicality question... Two particles move in the x-y plane. For t>=0, the position of particle A is x = (t-2)^2 and y = t-2 and the position of particle B is x = 3/2t - 2 and y = 3/2t - 4. At what time do the particles collide? I have already translated both equations into rectangular form and found that they intersect at the (x,y) point (4,2). Is this the answer I should give for "At what time do the particles collide?"? It doesn't seem to make sense with the question, but maybe that's just me...
Top 1 Answers
15 years ago
vlee1225
Favorite Answer
For t>=0, the position of particle A is x1 = (t-2)^2 and y1 = t-2 and the position of particle B is x2 = 3/2t - 2 and y2 = 3/2t - 4. At what time do the particles collide? Find t such that x1=x2: (t-2)^2 = 3/2t - 2 or t^2 - 4t + 4 = 3/2t -2 t^2 -5.5t + 6 = 0 ( t - 1.5) ( t - 4) = 0 ` ` ` ` or t = 1.5 or 4 and y1=y2: t-2 = 3/2t - 4. or 0.5t = 2 or t =4 so at t = 4, the two particles collide at x1=x2= 4 y1=y2= 2
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