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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

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 rocket boosters.

(a) Use a graphing calculator or computer to find the cubic polynomial that best models the velocity of the shuttle for the time interval t [0, 125]. Then graph this polynomial.

(b) Find a model for the acceleration of the shuttle and use it to estimate the maximum and minimum values of the acceleration during the first 125 seconds.

Event Time (s) Velocity (ft/s)
Launch 0 0
Begin roll maneuver 10 185
End roll maneuver 15 319
Throttle to 89% 20 447
Throttle to 67 % 32 742
Throttle to 104% 59 1325
Maximum dynamic pressure 62 1445
Solid rocket booster separation 125 4151

To determine

Part (a):

To find:

Cubic polynomial that best models the velocity data of the shuttle for the time interval tϵ[0,125] by using graphing calculator or computer then graph that polynomial.

Explanation

1) Concept:

Use the graphic calculator or computer to find the best fit cubic model for the given data, and then graph that polynomial.

2) Given:

Table gives the velocity data for the shuttle:

3) Calculation:

By using the graphic calculator or computer, the best fit cubic model for the above data is

vt=0

To determine

Part (b):

To find:

Find a model for the acceleration of the shuttle, and use it to estimate the maximum and minimum values of the acceleration during the first 125 seconds.

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