(Solved): When we estimate distances from velocity data, it is sometimes necessary to use times \( t_{0}, t_ ...

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 in order to install a new perigee kick motor in a communications satellite. The table provided gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use a right Riemann sum with six intervals indicated in the table to estimate the height \( h \) (in ft), above the earth's surface of the space shuttle, 62 seconds after liftoff. (Give the upper approximation available from the data.) \( h= \) \( \mathrm{ft} \)