1. ## parametric equation

Two objects move in the xy -plane. At time t, the position of object A is given by x = 5t - 5, y = -1t - k, and the position of object B is given by x = 3t, y = t2 - 2t - 1.

(a) Find the value of k so that the two objects collide.
(b) At what value of t do the objects collide?
(c) At what point do the objects collide?

2. Originally Posted by bluejewballs
Two objects move in the xy -plane. At time t, the position of object A is given by x = 5t - 5, y = -1t - k, and the position of object B is given by x = 3t, y = t2 - 2t - 1.

(a) Find the value of k so that the two objects collide.
(b) At what value of t do the objects collide?
(c) At what point do the objects collide?
setting the x coordinate equal we get.

$5t-5=3t \iff t=\frac{5}{2}$

Now we do the same thing with the y coordinates

$-1t-k=t^2-2t-1$ evaluate for t=5/2 and we get

$-\frac{5}{2}-k=\frac{25}{4}-5-1 \iff -10-4k=25-24 \iff k=\frac{11}{4}$

Now just plug in all this info to find the x and y coordinates