# Help with parametric equations?

• Nov 13th 2009, 07:16 PM
iheartthemusic29
Help with parametric equations?
Two particles move in the xy-plane. At time t, the position of particle A is given by x(t)=4t−4 and y(t)=2t−k, and the position of particle B is given by x(t)=3t and y(t)=t^2−2t−1.
Find k so that the particles are sure to collide.

My initial thought wast to take the derivatives of the equations, but then the k would just drop out, so that's not right.
Any suggestions? Thanks!
• Nov 13th 2009, 07:20 PM
Prove It
Quote:

Originally Posted by iheartthemusic29
Two particles move in the xy-plane. At time t, the position of particle A is given by x(t)=4t−4 and y(t)=2t−k, and the position of particle B is given by x(t)=3t and y(t)=t^2−2t−1.
Find k so that the particles are sure to collide.

My initial thought wast to take the derivatives of the equations, but then the k would just drop out, so that's not right.
Any suggestions? Thanks!

If the two particles collide, then surely they have the same x and y values...

So \$\displaystyle 4t - 4 = 3t\$ and \$\displaystyle 2t - k = t^2 - 2t - 1\$

From equation 1, \$\displaystyle t = 4\$.

So, when subbed into equation 2, we have

\$\displaystyle 8 - k = 7\$.

What is k?