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Problem 74 Medium Difficulty

On May 7, 1992, the space shuttle $ Endeavour $ was launched on mission STS-49, the purpose of which was to install a new perigee kick motor in an Intelsat communications satellite. The table gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rock boosters.

(a) Use a graphing calculator or computer to model these data by a third-degree polynomial.
(b) Use the model in part (a) to estimate the height reached by the $ Endeavour $, 125 seconds after liftoff.

Answer

a) $v(t)=0.00146137^{3}-0.115534 t^{2}+24.9817 t-21.2687$
b) $206,488 \mathrm{ft}$

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