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.

## Discussion

## Video Transcript

And this problem you have You have a table that helps you. Ah, uh, the one minute period ofthe car racing and so s made a distance by using the using the velocity at beginning offish time and in the violence has end of each time interval and ask you the last question. So for if you part you speaking we all the time and so each each time intervals ten seconds. So we put a tent here and we just have to some other velocities here. Ah, if one eighty two point nine plus, you have the value for table right plus one, sixty eight point zero plus one hundred six point six plus ninety nine point eight plus one twenty four point five plus one seventy six point one. Ah, But here as you and be careful that Ah, you'LL have to Ah, divide by thirty six hundred if you want to put the your union of smiles people So this time's measuring second and the thiss This philosophy is measured in miles per hour. So it's ours thirty six hundred seconds. So that's why I say And you have to divide by this a similar for Poppy This is your velocity, sir. This is your time off each time interval and we use the end. Like you said, the velocity as the end of time periods this estimate. So you just add up off them. Look at these value you can find on tech support. And for a similar reason you have divided by seriously House six hundred took as a unit, miles. And is this opera and overestimates well on its neither off them Because offering the lower estimate means means you use the largest and the smallest velocity at each time interval, for your estimation. And if we use beginning comment and pine and time eyes, neither off them.

## Recommended Questions