   Chapter 4.4, Problem 68E

Chapter
Section
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 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. 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:

The cubic polynomial that best models the velocity data of the shuttle for the timeinterval tϵ[0,125] by using a graphing calculator or computer

Explanation

1) Concept:

Use a T1 84 calculator to find the best fit cubic model for the given data

2) Given:

The table gives the velocity data for the shuttle:

3) Calculation:

Use Cubic Reg option of graphing calculator (TI 84 calculator) to find the best-fitting model for Cubic polynomial

From the given data, for given time interval tϵ[0,125], vt0, 4151

Steps to find cubic polynomial using TI 84 calculator:

Step 1: Enter Stat Editor, then Press STAT.

Step 2: Select Edit to input data into lists.

Step 3: When there is data in list from previous work, it needs to be cleared before work is continued

Step 4: Enter data in L1 and L2.

Step 5: Press 2nd STAT PLOT (this is the Y= key). At this point, need to check if the plots are on or off.  All plots should be off except the one with which you are working.

Step 6: Press ENTER to select Plot 1.

Step 7: Turn Plot1 ON by highlighting the word ON and pressing ENTER.

Step 8: Select the ‘Cubic plot’ for plot Type

To determine

Part (b):

To estimate:

The height reached by the Endeavour 125 seconds after the liftoff using the model in part (a)

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