Math problem: parametric equations!?

Question

Two objects move in the xy -plane. At time t, the position of object A is given by x = 9t - 9, y = -3t - k, and the position of object B is given by x = 7t, y = t2 - 2t - 1.
(a) Find the value of k so that the two objects collide.
k=?
(b) At what point do the objects collide?
x=?
y=?

Answer 1

for the objects to collide, at some time t, their x and y values must coincide.

for x:
9t - 9 = 7t
t = 4.5

for y:
-3t - k = t^2 -2t - 1
t^2 + t -1 + k = 0
20.25 + 4.5 -1 + k = 0
k = -23.75

x = 9t-9 = 9*4.5-9 = 31.5
x = 7t = 7*4.5 = 31.5 check

y = -3t - k = -3(4.5) + 23.75 = -10.25
y = t^2 - 2t -1 = 20.25 -9 - 1 = 10.25 check

Answer 2

Hello,

To collide the x-values and the y-values have to be equal so
7t = 9t -9 and t^2-2t-1 = -3t -k now from the first equation we have t = 9/2 so put it into the second one giving us (9/2)^2 -2(9/2) -1 = -3(9/2) -k so 81/4 -9 -1 = -27/2 -k multiply by 4 and we have 81 -36 -4 = -54 - 4k or 41 = -54 -4k so -4k = 95 k = -95/4. Now put this into the original equations with t = 9/2 to find x and y.

These values look a little strange, so check my math please.

Hope This Helps!