The prospect of death focuses the mind. Suppose you are in a plane at an altitude of $30000$ ft when the engines fail. The pilot trims the plane for an efficient glide at $300$ knot at a descent rate of$\mathrm{ 3}000$ ft$/$min$.$ She will flare the plane to decrease the speed and descent rate just before landing. Use the results of the previous problem, and round numbers. If you want to be a steely$-$eyed aeronaut, don$’$t use your calculator, you need both hands for the controls.

$($a$)$ What is the slope of the glide?

$($b$)$ How far can you glide, in nautical miles?