A rectangular structure carries clocks at its four corners. The clocks are synchronized in the structure’s rest frame, in which it has length L =4ft and width W = 3ft. In our laboratory frame the rectangle is moving in the positive x direction at speed v = 0.8c. As the clock at the lower left corner of the rectangle flies past a laboratory laser, the laser fires once, freezing the clock display at zero nanoseconds. The same laser pulse then strikes the rectangle’s upper right clock, disabling that clock too. Determine the reading on the upper right clock after it is disabled.
The Attempt at a Solution
In the rectangle's rest frame (taken to be coincident with the lab frame at t=0) the laser beam travels along its diagonal with a length of 5 ft. But from the lab frame the length of the rectangle is Lorentz contracted from 4 ft to 2.4 ft. In the time it takes the light to reach the upper right corner, call it ##t## ,the rectangle will have moved ##0.8ct## so the overall distance the light has to travel is the hypoteneuse of a triangle with length ##2.4 +0.8ct## (this is the part I am unsure of) and height 3 ft. The speed of light is the same in all reference frames so ##c = 5/\tau = d'/t## from which ##t## can be found.