From work-energy theorem:

Work done = gain in kinetic energy.

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

Work:

$\overline{)\begin{array}{rcl}{\mathbf{w}}& {\mathbf{=}}& \mathbf{F}\mathbf{\xb7}\mathbf{d}\end{array}}$, where F is force and d is distance.

The thrust produced by a lone jet engine generates a force of F = 84000 N. Which requires the airplane (with a mass of m = 9600 kg) a distance of d = 0.74 km to take off

Part (a) What is the take-off speed of the airplane vt in m/s?

Part (b) How far in meters would you need to depress a giant spring k = 100,000 N/m in order to launch the airplane at the same speed without help from the engine?

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