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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Okay, so we have all six of equal choose. They're all times 0.56 to 5 was 10.8 times 0.5 plus 18.14 That's 19 four times five. What's 69 points? Four times reports five sums degree or 50.7 feet? Well, we have our at six. That's equal to they report 56.2 plus the dope. It's fine. Times 10 feet plus zero point fire times 14.9 18.17 point five butts, 19 points boards. That's five plus 28.2. What's five? Yeah, this is 44 48 Speaks. So our upper estimates is restaurant overestimate. Its 44.8 feet and lower estimate is 34.7 feet.

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