When we estimate distances from velocity data, it is sometimes necessary to use times to, t1, t2, t3, ... that are not equally spaced. We can still estimate distances using the time periods At; = t; - tj - 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 o the space shuttle, 62 seconds after liftoff. (Give the upper approximation available from the data.) ft Event Time (s) Velocity (ft/s) Launch Begin roll maneuver 10 180 End roll maneuver 15 319 Throttle to 89% 20 442 Throttle to 67% 32 742 Throttle to 104% 59 1325 Maximum dynamic pressure 62 1453
When we estimate distances from velocity data, it is sometimes necessary to use times to, t1, t2, t3, ... that are not equally spaced. We can still estimate distances using the time periods At; = t; - tj - 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 o the space shuttle, 62 seconds after liftoff. (Give the upper approximation available from the data.) ft Event Time (s) Velocity (ft/s) Launch Begin roll maneuver 10 180 End roll maneuver 15 319 Throttle to 89% 20 442 Throttle to 67% 32 742 Throttle to 104% 59 1325 Maximum dynamic pressure 62 1453
Calculus: Early Transcendentals
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![When we estimate distances from velocity data, it is sometimes necessary to use times \( t_0, t_1, t_2, t_3, \ldots \) that are not equally spaced. We can still estimate distances using the time periods \( \Delta t_i = t_i - t_{i-1} \). 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. (Give the upper approximation available from the data.)
\[ h = \underline{\hspace{3cm}} \, \text{ft} \]
| Event | Time (s) | Velocity (ft/s) |
|------------------------------|----------|----------------|
| Launch | 0 | 0 |
| Begin roll maneuver | 10 | 180 |
| End roll maneuver | 15 | 319 |
| Throttle to 89% | 20 | 442 |
| Throttle to 67% | 32 | 742 |
| Throttle to 104% | 59 | 1325 |
| Maximum dynamic pressure | 62 | 1453 |
| Solid rocket booster separation | 125 | 4052 |
This table shows a series of events with their corresponding times and velocities. The challenge is to estimate the height of the shuttle at 62 seconds using these velocity data points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a15759c-8b82-438f-9d6a-36f728df4f17%2F8b009dae-bb15-4e5a-bbee-5d297c0d11fc%2F3rsnkel_processed.jpeg&w=3840&q=75)
Transcribed Image Text:When we estimate distances from velocity data, it is sometimes necessary to use times \( t_0, t_1, t_2, t_3, \ldots \) that are not equally spaced. We can still estimate distances using the time periods \( \Delta t_i = t_i - t_{i-1} \). 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. (Give the upper approximation available from the data.)
\[ h = \underline{\hspace{3cm}} \, \text{ft} \]
| Event | Time (s) | Velocity (ft/s) |
|------------------------------|----------|----------------|
| Launch | 0 | 0 |
| Begin roll maneuver | 10 | 180 |
| End roll maneuver | 15 | 319 |
| Throttle to 89% | 20 | 442 |
| Throttle to 67% | 32 | 742 |
| Throttle to 104% | 59 | 1325 |
| Maximum dynamic pressure | 62 | 1453 |
| Solid rocket booster separation | 125 | 4052 |
This table shows a series of events with their corresponding times and velocities. The challenge is to estimate the height of the shuttle at 62 seconds using these velocity data points.
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