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

$ \Delta 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.

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## Video Transcript

here, give you the oil leaking rate and ask you to find the finds. Ah, it's a total amount of oil that leaks out so again the time into those two hours. And what is the lower estimate? The lower estimate for each in time interval we use the smallest possible e great Assauer estimate so far is that from zero to two, we pick seven point six against the table. It's on your textbook. From two to four. We pick a six point eight six point two from six to eight. We put five point seven from eight to ten. We pick five points. Three a simile for up her ah each interval pictures the largest leaking rate for for our estimate and each time into those two hour. By the way, the unit's leader here and so the first one should be a point seven. The second one seven point six six point eight six point two five point seven

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