A train with skylights has the same rest length as a tunnel. The train goes through the tunnel at high speed. In the train’s frame, the tunnel is contracted to be shorter than the train. As the train passes through the tunnel two passengers, Wendy at the front and John at the rear, glance up at the same moment, and both of them see blue sky. In the tunnel’s frame, the train is contracted to be shorter than the tunnel. How can the two passengers look up and both see blue sky?

. A) How fast would a motorist have to travel for a yellow traffic light (λ = 590. nm) to appear  green (λ =500. nm) to him due to the Doppler shift? B) Would the motorist be traveling towards  or away from the traffic light?

George is in a spaceship, speeding away from planet Earth at , where is the speed of light in a vacuum. Anna is on George's ground crew, and she sends out a communication signal to George. Since Anna's communication signal is a radio wave, it is electromagnetic and travels at a speed of relative to Anna. From George's perspective, Anna's signal is approaching him at a speed of? c 0.5c 2c 0

As shown in the figure, a stationary mirror is mounted in a reference frame S and a space shuttle moves toward the mirror at a speed v = 0.590c relative to the reference frame S. The instant the shuttle is a distance d = 5.00 × 10¹0 m from the mirror (as measured by an observer in S), it emits a light pulse that travels to the mirror and is reflected back to the shuttle. Determine the total travel time (in s) for the light pulse as seen by the following. (a) an observer in the S reference frame S (b) an observer on the shuttle S What If? If the light beam has an initial wavelength of 530 nm, determine the shift (in nm) in the wavelength of the light beam as measured by the following (use + for an increase and decrease). (c) an observer in the S frame nm Mirror (d) an observer on the shuttle nm for a

Observer A sees two events at the same place (Ax = Ay = Az = 0) and separated in time by Ar = 10-6 s. A second observer B sees them to be separated by Ar' = 2 × 10-6 s. What is the separation in space of the two events according to B? What is the speed of B relative to A?

1. Some jets emitted by galaxies, for astronomical distances large enough, can appear to travel faster than the speed of light c, through our line of sight. Suppose that a distant galaxy, AB15, is moving with speed v at an angle e with respect to the earth and it emits two light rays separated by a time At in its local time. show that a) The time interval on earth in which the two light rays are emitted is given by Atr = At(1– B cos 0) b) The apparent speed of AB15 measured by an observer on earth is ArT VA = Att B sin e 1-B cos 0 %3D c) For B = 0.75, calculate the value of 0 for which Va =c

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Events 1 and 2 are exploding firecrackers that each emit light pulses. In the reference frame of the detector, event 1 leaves a char mark at a distance 3.40 m from the detector, and event 2 leaves a similar mark at a distance 2.10 m from the detector. If the two events are simultaneous in the reference frame of the detector and occur at instant t = 0, at what instant of time will each light pulse be detected?

Your video analysis of the motion of a marble gives it position in frame 23 as (x23, 923) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, Y24) = (0.122 m, 0.112 m). You esti- mate that you can measure the x and y positions with uncertainty +0.003 m. The frame rate of the video is 30 frames/s, which means the time interval between frames is At = 0.033 333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this prob- lem, use (At) = 1 x 10-6 s. The mass of the marble is (2.031 +0.001) x 10-2 kg. Calculate the following quantities: 1. The value of the velocity component U = Xi+1Xi At and its uncertainty, Yi+1 Yi = and its uncertainty, At 2. The value of the velocity component vy 3. The value of the velocity magnitude v = 4. The value of the momentum component p 5. The value of the momentum component Py = muy and its uncertainty, and 6. The value of the kinetic energy K = =mv² = m(v²+v²) and its uncertainty. v2+2 and its uncertainty, = mv, and…