When we estimate distances from velocity data, it is sometimes necessary to use times to, t,, t2, t3, ... that are not equally spaced. We can still estimate distances using the time periods at, = t; - t; - 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. Event Time (s) Velocity (ft/s) Launch Begin roll maneuver 10 185 End roll maneuver 15 319 Throttle to 89% 20 447 Throttle to 67% 32 742 Throttle to 104% 59 1325 Maximum dynamic pressure 62 1445 Solid rocket booster separation 125 4151

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Chapter4: Motion In Two And Three Dimensions
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I need help solving the final velocities for the first two intervals 

Tutorial Exercise
When we estimate distances from velocity data, it is sometimes
necessary to use times to, t1, tz, t3, ... that are not equally spaced.
We can still estimate distances using the time periods at, = t; - tj - 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.
Event
Time (s) Velocity (ft/s)
Launch
Begin roll maneuver
10
185
End roll maneuver
15
319
Throttle to 89%
20
447
Throttle to 67%
32
742
Throttle to 104%
59
1325
Maximum dynamic pressure
62
1445
Solid rocket booster separation
125
4151
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
O and ends at t
10, so its width
%3D
%|
is
At = 10
2 10 .
Step 2
The second interval begins at t = 10 and ends at t = 15, so its
width is
At2 =
Step 3
The final velocities for the first two intervals are, respectively,
x and v2 =
V1 =
5
Transcribed Image Text:Tutorial Exercise When we estimate distances from velocity data, it is sometimes necessary to use times to, t1, tz, t3, ... that are not equally spaced. We can still estimate distances using the time periods at, = t; - tj - 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. Event Time (s) Velocity (ft/s) Launch Begin roll maneuver 10 185 End roll maneuver 15 319 Throttle to 89% 20 447 Throttle to 67% 32 742 Throttle to 104% 59 1325 Maximum dynamic pressure 62 1445 Solid rocket booster separation 125 4151 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 O and ends at t 10, so its width %3D %| is At = 10 2 10 . Step 2 The second interval begins at t = 10 and ends at t = 15, so its width is At2 = Step 3 The final velocities for the first two intervals are, respectively, x and v2 = V1 = 5
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