When we estimate distances from velocity data it is sometimes necessary to use t

Question

When we estimate distances from velocity data it is sometimes necessary to use times to, ti, t2, t3,... that are not equally spaced. We can still estimate distances using the time periods Atti - tj- 1. The following table gives the velocity data for a shuttle between liftoff and the jettisoning of the solid rocket boosters Event Launch Begin roll maneuver End roll maneuver Throttle to 89% Throttle to 67% Throttle to 104% Maximum dynamic pressure Solid rocket booster separation Time(s) Velocity(ft/s) 0 10 15 20 32 59 62 125 0 185 319 447 742 1325 1445 4151 Use these data to estimate the height, h, above Earth's surface of the space shuttle, 62 seconds after liftoff. (Give the upper approximation available from the data.) Part 1 of 4 We can obtain an upper estimate for the height by using the final velocity for each time interval The first interval begins at t 0 and ends at t- 10, so its width is

Explanation / Answer

As the question staes, upper bound can be found out by using final velocity of each interval

(0 - 10) = 185 ft/s

10 - 15 = 319 ft/s

15-20 = 447 ft/s

20-32 = 742 ft/s

32-59 = 1325 ft/s

59-62 = 1445 ft/s

Therefore,

Upper bound of height after 62 seconds

hupper bound = (10*185) + (5*319) + (5*447) + (12*742) + (27*1325) + (3*1445)

hupper bound = 54694 ft

time width from t = 0 to t = 10 is t = 10

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