Pictures of SS Enterprise, being far away and approaching or being far away and receding · RMPH 2013 #4

Physics

Problem

Description of the situation: Star Ship Enterprise has on each of the two warp engines a succession of five collinear, equidistant, numbered, beacons as shown in the figure (for the propeller on right side). When traveling, SS Enterprise moves with constant speed

\vec{v}

so that, for the questions that follow, beacons located on a propeller are always on the same line that is Ox axis of the coordinate system. In the situation room of another spacecraft which is at rest and which oversees the SS Enterprise, are analyzed the images of line of beacons. The images are taken by a camera with the aperture located at the point

(0,d)

in the orthogonal coordinate system shown in the inset in figure above. An image of line of beacons is produced by light rays that arrive simultaneously at camera aperture that opens for a short time. On a picture of SS Enterprise at rest, the length of line of beacons is L. In the problem, the beacons can be considered as points. The speed of light is

c = 3.00 \times 10^8 \text{m} \cdot \text{s}^{-1}

. Employ the quantities

\beta = v/c

and

\gamma = 1/\sqrt{1-\beta^2}

, if they help to simplify your result. Task No. 4 - Pictures of SS Enterprise, being far away and approaching or being far away and receding Camera takes a picture when SS Enterprise is approaching from far away and another image when the ship (and the beacons line) is far away and receding. On one of these images the apparent length of the line of beacons is 160m and the other is 600m. 4.a. Decide which of the following statements is correct. i. Apparent length is 200m on the image of "approaching" ship and 600m on the image of "receding" ship. ii. Apparent length is 600m on the image of "approaching" ship and 200m on the image of "receding" ship. Write in the appropriate box in the answer sheet the letter corresponding to the answer you think is correct. Briefly justify your choice. 4.b. Determine the speed v of the ship. 4.c. Calculate the value of length of the beacons line at rest. 4.d. Calculate the value of length of the beacons line on the symmetric picture, described at task no. 3.a.

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