A college student was tracking an unidentified flying object, and made several o

Question

A college student was tracking an unidentified flying object, and made several ob- servations. We will use t for the time of the observation, beginning at t 0 with the first sighting. We will use the vector-valued function Flt) to describe the position of the object, and T(t) to describe its velocity. The observer records the following data on the object. You may consider the observer to be at the origin of this coordinate system, and the units to be in meters. t) 0| 200,--10, 738.2) | (0, 0.05,-12.6) 3 (191.07,-9.7,678.8) -5.91,0.048,-7.2) 8 |( 12| (72.47,9.1,695) | (-18.64, 0.018,9) 139.94,-93, 651.8) (-14.35, 0.035, 1.8) 1. Does the object appear to move generally right-to-left, or left-to-right? Ex- plain. 2. Is the object moving closer to the top of an abandoned building located at (65,-9,20), or farther away? Explain. 3. Estimate the distance traveled by the object. Is your estimate an underestimate, or an overestimate? 4. Is re) parameterized by arc length? Explain. 5. Assuming a(O) 8 for every t observed, what is the maximum possible curvature of the object's path? What information would you need to estimate the torsion?

Explanation / Answer

1. After plotting graph, we can see that x and z coordinate of r(t) decreases and moves right to left and y coordinate increases and moves towards right to left. So object appear to mmovve generally right to left..

2. From given data it is clear that object moving closer to the top of an abandoned building located at (65,-9,20) as given last coordinate of r(t) is (72.47,-9.1,695) and it is moving towards (65,-9,20).

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