Concept explainers
When we estimate distances from velocity data, it is sometimes necessary to use times t0, t1, t2, t3, … that are not equally spaced. We can still estimate distances using the time periods Δti = ti − ti − 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 |
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Single Variable Calculus: Early Transcendentals, Volume I
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