Question

The Navy wants a new airplane launcher for their aircraft carriers that is basically a large spring and your job is to determine the necessary spring constant. The launcher pushes the plane for a short distance along a much longer runway. During that same time, the plane's jet engines supply a constant thrust force for the entire length of the runway. The planes need to have a minimum velocity by the time they reach the end of the runway in order to take off successfully.

(a) What is the algebraic expression for the spring constant of the launcher in terms of the mass of the plane (M), the minimum take-off speed of the plane (V), the thrust force by the engines (F), the length of the runway (L), the distance that the spring pushes the plane (D), and the gravitational field strength (g)? [Note: Don't enter an equation like "x=blah". Just enter the "blah" part. All letters are capital except for "g".]