Chapter 12.1, Problem 65E

Air drop—inverse problem A plane traveling horizontally at 100 m/s over flat ground at an elevation of 4000 m must drop an emergency packet on a target on the ground. The trajectory of the packet is given by

$\begin{array}{ccc}x=100t,& y=-4.9t^2+4000,& \text{for}t\ge 0,\end{array}$

where the origin is the point on the ground directly beneath the plane at the moment of the release. How many horizontal meters before the target should the packet be released in order to hit the target?