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# Problem: The thrust produced by a single jet engine creates a force of F = 84000 N. It takes the jet (with a mass of m = 5200 kg) a distance of d = 0.78 km to take off.(a) What is the take-off speed of the jet vt in m/s?(b) How far in meters would you need to depress a giant spring k = 100,000 N/m in order to launch the jet at the same speed without help from the engine?

###### FREE Expert Solution

This is a work-energy relation problem because we have forces and mass.

Work done by a constant force:

$\overline{){\mathbf{W}}{\mathbf{=}}{\mathbf{F}}{\mathbf{×}}{\mathbf{d}}}$

Kinetic energy:

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

The potential energy of a compressed spring:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}}$

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###### Problem Details

The thrust produced by a single jet engine creates a force of F = 84000 N. It takes the jet (with a mass of m = 5200 kg) a distance of d = 0.78 km to take off.

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

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