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 $\Delta t_i = t_i-t_{i-1}.$ 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. $$\begin{array}{|c|c|c|}\hline \textrm{Event} & \textrm{Time}\ (s) & \textrm{Velocity}\ (ft/s) \\ \hline \textrm{Launch} & 0 & 0 \\ \hline \textrm{Begin roll maneuver} & 10 & 185 \\ \hline \textrm{End roll maneuver} & 15 & 319 \\ \hline \textrm{Throttle to 89 percent} & 20 & 447 \\ \hline \textrm{Throttle to 67 percent} & 32 & 742 \\ \hline \textrm{Throttle to 104 percent} & 59 & 1325 \\ \hline \textrm{Maximum dynamic pressure} & 62 & 1445 \\ \hline \textrm{Solid rocket booster separation} & 125 & 4151 \\ \hline \end{array}$$ Use these data to estimate the height (in feet) above Earth's surface of the space shuttle Endeavour, 62 seconds after liftoff. In your estimate, use right endpoints.

Height at 62 seconds after takeoff $\approx$ feet