Tutorial Exercise .. that When we estimate distances from velocity data, It is sometimes necessary to use times to 4, ty, ty are not equally spaced. We can still estimate distances using the time periods At, - , - 11. 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. Event Time (s) Velocity (ft/s) Launch 0 0 Begin roll maneuver 10 175 End roll maneuver 15 309 Throttle to 89% 20 457 Throttle to 67% 32 732 Throttle to 104% 59 1,320 Maximum dynamic pressure 62 1,435 Solid rocket booster separation 125 4,141 Use a right Riemann sum with six intervals indicated in the table to estimate the height , above the earth's surface of the space shuttle, 62 seconds after liftoff. Step 1 Let v represent the velocity of the space shuttle at a time t. Recall that a right Riemann sum with six intervals is given by the following Let (t) represent the velocity of the space shuttle at a time t. Recall that a right Riemann sum with six Intervals is given by the following. (,)At, In this case the intervals are not evenly spaced, so At, will differ for each interval such that At = t; -1,-1. In other words, we will use the following. Kelle, – t, -1) I=1 Complete the following table to identify all the needed values to apply this Riemann sum. Note that we are looking for the height after 62 seconds, so we do not need to consider the interval [62, 125). Time (s) Velocity (ft/s) ty t-4-1 0 0 0 0 10 175 1 10 15 309 2 X 20 457 اليا 60 32 732 4 128 X 59 1,320 5 295 XX 62 1,435 6 372 125 4,141 7