When we estimate distances from velocity data, it is sometimes necessary to use

Question

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 Ati = ti-ti-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 liftof. Time (s) Velocity (ft/s) Event Launch Begin roll maneuver End roll maneuver Throttle to 89% Throttle to 67% Throttle to 104% Maximum dynamic pressure Solid rocket booster separation 125 0 10 15 20 32 0 185 319 447 742 1325 1445 4151 62 Step 1 We can obtain an upper estimate for the height by using the final velocity for each time interval The first interval begins at t 0 and ends at t-10, so its width is 10 Step 2 The second interval begins at t 10 and ends at t-15, so its width is Step 3 The final velocities for the first two intervals are, respectively, V1185 and V2=92.5

Explanation / Answer

Velocity V2 = 319 - 185 = 134 ft/s.

  

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