A) what is the slope of the telescope 5, 10, and 20 seconds after tge plane passes overhead? B)what is the slope of the telescope t seconds after the plane passes overhead ?
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In t seconds the plane moves 300t feet further east. The plane was initially at an altitude of 5000 feet. What we have is a right triangle with the long leg=5000 and the short leg=300t. As the plane moves the telescope is tilted further and further away from the vertical. The slope (tangent) of this angle is 300t/5000=3t/50.

(A) Now we can put t=5, 10 and 20: 0.3, 0.6, 1.2. The slopes relative to the ground are the inverses of these:

10/3, 5/3, 5/6. The corresponding angles are 73.30, 59.04, 39.81 degrees. The angles from the vertical are these angles subtracted from 90 degrees: 16.70, 30.96, 50.19 degrees.

(B) The slope (from the ground, or angle of tilt of the telescope) is 50/3t or arctan(50/3t) (same as tan^-1(50/3t)).

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