Two moving bodies

Question

I'm doing parametric equations, however I'm stuck on last question from my lab sheet. Can someone help?

Consider two moving bodies whose positions are given by the following sets of parameterised equations: Body 1: x = 7t - 3 y = 5 + t - t ^2 Body 2: x = 6 - 2t y = (t - 3)^2 + 1

Will these two bodies hit each other? If, so what's the position of the collision?

Thanks!

Answer 1

Hint:

The bodies do collide if they can have the same abscissa and ordinate at the same time.

They have the same abscissa when

$$7t-3=6-2t.$$

You should be able to finish.

$$t=1,\\x_1=x_2=4,\\y_1=y_2=5.$$