A video camera is stationed 50 feet from a road that is part of a parade route t
ID: 3288276 • Letter: A
Question
A video camera is stationed 50 feet from a road that is part of a parade route to film the passing parade. Assume the parade floats are traveling the route towards the camera at a speed of 15 mi/hr. (a) At what rate must the camera rotate to follow the parade floats when they are 25 feet from the point P on the road closest to the camera? At the instant they pass point P? (b) At what rate must the camera's focus adjust to film the floats clearly (that is, at what rate does the distance from the flat to the camera change) when the floats are 200 feet from point P? When they are 50 feet from point P?Explanation / Answer
I will not answer all for lack of time; Howeverr, I will clue you in on the rotational spped of camera at instant the Parade passes point P. At that point the camera is 50ft. from the road and parade. You can compute the distance the perade is from the camera in the other cases by using pathogoren theorem. At 50 ft. distancemust move atparade speed. At 15MPh, the parade is moving at 22ft./sec.
The circumference of the circle at that point from the camera=100 x pi=314.16 ft; At 22ft/sec the camera rotates as a speed of 14.28 revolutions second at aspeed of 22ft./sec. Aradian =57.3 degrees so 1 revolution =360/57.3=6.283; therefore 14.28 rev/sec x 6.283Radians per revolutions=14.28 ,sec. On changing focus's, you just need to compute the distance traveled from point a to point b by the parade as compared to the change in distance between the parade and camera at these points. iechange in distance from camera over time parade took to travel this distance will give you thecamera focus: Example Distanc Parade travels (ft/sec x distance0 under the change in distance the camera must focus during the time should give you rate of change in focus.
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