“3…2…1… Liftoff!” A rocket launches from the ground at time t = 0 seconds. An ob
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Question
“3…2…1… Liftoff!” A rocket launches from the ground at time t = 0 seconds. An observer 2000 meters away tracks the rocket with a telescope. The rocket’s height is given by h, in meters, and the angle between the telescope and the ground is given by , in radians.
“Houston, we have a problem…” A Calculus problem, that is!
dh/dt
d/dt
400 m/s
0.17 rad/sec
600 m/s
0.17 rad/sec
800 m/s
0.11 rad/sec
1000 m/s
0.07 rad/sec
2) In your own words, what does dh/dt tell us about the rocket? Include units.
3) Determine the value of d2 h/ dt2 based on the table in Part 1. Explain how you arrived at this value. Additionally, using your own words, what does this value tell us about the rocket? Include units in your explanation.
4) In your own words, what does d/dt tell us? Include units.
5) Let c be the distance between the rocket and the observer. Answer the following:
a) Determine the rate at which c is changing with respect to time when t = 6 seconds by relating c and . Use the applet to find some of the necessary values. Show your work in a manner consistent with that demonstrated in class and state your final conclusion using a whole sentence that includes units.
d) Again, let c be the distance between the rocket and the observer. Determine the rate at which c is changing with respect to time when t = 4 seconds by relating c and h. Use the applet to find some of the necessary values. Show your work in a manner consistent with that demonstrated in class and state your final conclusion using a whole sentence that includes units.
tdh/dt
d/dt
2 200 m/s 0.1 rad/sec 4400 m/s
0.17 rad/sec
6600 m/s
0.17 rad/sec
8800 m/s
0.11 rad/sec
101000 m/s
0.07 rad/sec
Explanation / Answer
2) In the table dh/dt means the rate of change of distance meter per sec
3)d^2h/dt^2 means rate of change of velocity
its values will be
= 400-200/4-2 =200/2=100 meter sec^2
4) d theta/dt means rate of change of angle in radian per sec
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