Question

The path of 2 objects are described by the parametric equations below.

object 1: 

x = t

y = t² + 2

object 2:

 x= 2t +1

y= t + 4

Find when and where the objects collide.

They collide at (_,_) when t = 

.

Answer 1

Graph of object 1 (G1)

$x=t\\$ .......(1)

$y=t^2+2$ .........(2)

Putting 1 in 2 we get,

$\boxed{y=x^2+2}$ ..…....(G1)

Now Graph of object 2 (G2)…

$x=2t+1$ ..........(3)

$y=t+4$ ...........(4)

Putting (3) in(4)..we get,

$\boxed{y={x+7\over 2}}$ ............(G2)

Now we find intersection of G1 and G2,

We get,

$\boxed{y=4.25, X=1.5}$

As point of intersection,

For t we put y coordinates of both objects are equal,

$t^2+2=t+4$

we get,

t=-1,2

But -1 can't be expected because t can't be negative.

So $\boxed{t=2}$ is answer.

They collide at (1.5,4.25) when t = 2.