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 500 500 centimeters away. Its flight path is given by parametric equations {x=100ty=80t16t2 \begin{cases} x &=& 100t \\ y &=& 80t - 16t^2 \end{cases} where tt is time in seconds.

Two seconds later Jingle launches an interceptor pie from his location with the flight path {x=500500(t2)y=K(t2)16(t2)2 \begin{cases} x &=& 500 - 500(t-2) \\ y &=& K(t-2) - 16(t-2)^2 \end{cases} Find the value of KK which will guarantee that the interceptor pie will hit its target (the pie thrown by Twinkle).

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