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, a space shuttle was launched on a mission, the purpose of which was to install a new motor in a satellite. The table provided gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use these data to estimate the height, h, above Earth's surface of the space shuttle, 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 We can obtain an upper estimate for the height by using the final velocity for each time interval.
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, a space shuttle was launched on a mission, the purpose of which was to install a new motor in a satellite. The table provided gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use these data to estimate the height, h, above Earth's surface of the space shuttle, 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 We can obtain an upper estimate for the height by using the final velocity for each time interval.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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, a space shuttle was launched on a mission, the purpose of which was to install a new motor in a satellite. The table provided gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use these data to estimate the height, h, above Earth's surface of the space shuttle, 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 |
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
Δt1
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