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

Work done by a constant force:

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

Kinetic energy:

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

The potential energy of a compressed spring:

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

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?

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Our tutors have indicated that to solve this problem you will need to apply the Work By Variable Forces (Springs) concept. You can view video lessons to learn Work By Variable Forces (Springs). Or if you need more Work By Variable Forces (Springs) practice, you can also practice Work By Variable Forces (Springs) practice problems.