Chapter 10.6, Problem 65PE

For a short interval of time, a military supply plane flies on a hyperbolic path given by the equation $\frac{y^2}{{122.5}^2}-\frac{x^2}{{100}^2}=1;y\ge 0,$ where $x$ and $y$ are measured in meters.

a. What are the coordinates of the point on the flight path closest to the ground?

b. When the plane reaches its closest point to the ground, it drops a bag of supplies to people on the ground. Assuming that the plane is traveling $200\text{m/sec}$ due east at the time of the drop, write parametric equations representing the path of the bag as a function of the time $t$ (in sec) after the drop.

c. Determine the coordinates of the point where the bag hits the ground.