The Clown's Interceptor Pie
Algebra
Level
2
Two clowns, Twinkle and Jingle, are throwing pies at each other. Twinkle throws a pie toward Jingle from \( 500 \) centimeters away. Its flight path is given by parametric equations \[ \begin{cases} x &=& 100t \\ y &=& 80t - 16t^2 \end{cases} \] where \(t\) is time in seconds.
Two seconds later Jingle launches an interceptor pie from his location with the flight path \[ \begin{cases} x &=& 500 - 500(t-2) \\ y &=& K(t-2) - 16(t-2)^2 \end{cases} \] Find the value of \(K\) which will guarantee that the interceptor pie will hit its target (the pie thrown by Twinkle).
by
Arron Kau