## Question

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 Δt_{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 = ft

Event | Time (s) | Velocity (ft/s) |

Launch | 0 | |

Begin roll maneuver | 10 | |

End roll maneuver | 15 | |

Throttle to 89% | 20 | |

Throttle to 67% | 32 | |

Throttle to 104% | 59 | |

Maximum dynamic pressure | 62 | |

Solid rocket booster separation | 125 |