ps1 - P207 - Fall 2007 Solutions Assignment 1 1 The...

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Unformatted text preview: P207 - Fall 2007 Solutions Assignment 1 1 The apparent size of the elevator is proportional to the angle subtended . We see from the diagram that tan = h/d where h is the height of the elevator and d is the distance. Since the height is always much h d less than the distance, we can use the small angle approximation for the tangent and write that h d (a) The angular size of elevator at various distances is given in the table distance angular size angular size (small angle approximation) (exact) d[km] [rad] h/d [rad] = tan- 1 ( h/d ) 8 5 10- 3 5 . 000 10- 3 4 1 10- 2 1 . 000 10- 2 2 2 10- 2 2 . 000 10- 2 1 4 10- 2 3 . 998 10- 2 0.5 8 10- 2 7 . 983 10- 2 0.25 1 . 6 10- 1 1 . 587 10- 1 1 (b) Angular size of 40m grain elevator vs distance. 0.05 0.1 0.15 0.2 2000 4000 6000 8000 10000 [rad] distance [m] h/d 2 (c) Log plot of angular size of 40m grain elevator vs distance. The log 0.001 0.01 0.1 1 10 2000 4000 6000 8000 10000 [rad] distance [m] h/d plot is very nearly a straight line over distances large compared to the height of the object. Therefore, the angular size is an approximately exponential function of the distance....
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ps1 - P207 - Fall 2007 Solutions Assignment 1 1 The...

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