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 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, 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

Explanation / Answer

These type of problems are generally easy.

We are given speed at various time.

Since we have to upper approximate the distance and the speed is increasing over time in the data, we will linearly approximate it.

So between the time 0 to 10 sec we will approximate the rocket was flying with 180 ft/s. Similarly for 10 to 15 we will assume its flying with 319 and similarly for other time slots.

Net Distance Travelled = Partwise sum of Distances in the time slots

Distance = Speed * Time

So

Distance = 180 * (10-0) + 319 * (15-10) + 442 * (20-15) + 742 * (32 - 20) + 1217 * (59-32) + 1453 * (62-59)

Distance = 51727 fts.

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