Two clowns, Twinkle and Jingle, are throwing pies at each other. Twinkle throws a pie toward Jingle from 500500 centimeters away. Its flight path is given by parametric equations
\begin{cases} x &=& 100t \\ y &=& 80t - 16t^2 \end{cases}
{ x
y
=
=
100t
80t−16t 2
where tt is time in seconds.
Two seconds later Jingle launches an interceptor pie from his location with the flight path
\begin{cases} x &=& 500 - 500(t-2) \\ y &=& K(t-2) - 16(t-2)^2 \end{cases}
{ x
y
=
=
500−500(t−2)
K(t−2)−16(t−2) 2
Find the value of KK which will guarantee that the interceptor pie will hit its target (the pie thrown by Twinkle).
