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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

When we estimate distances from velocity data, it is sometimes necessary to use times t 0 , t 1 , t 2 , t 3 , ... that are not equally spaced. We can still estimate distances using the time periods t i = t i t i 1 . For example, 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, provided by NASA, gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use these data to estimate the height above the earth’s surface of the Endeavour, 62 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

To estimate:

The height

Explanation

1) Concept:

A=limni=1nfxix

where,

x=b-an & xi=a+ix

2) Calculation:

Let us use the given data to estimate the height above the earth’s surface of the Endeavour, 62 seconds after liftoff.

It is given that

ti=ti-ti-1

So, calculate the ti for each interval

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