# C when the newspaper is thrown to the side 80 ms y y

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(c) When the newspaper is thrown to the side, 8.0 m/s. y y u u = = Also, 0 m/s 5.0 m/s 5.0 m/s x x u u v = + = + = Thus the newspaper’s speed is ( ) ( ) 2 2 2 2 5.0 m/s 8.0 m/s 9.4 m/s x y u u u = + = + =

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37.6. Model: Assume the spacecraft is an inertial reference frame. Solve: Light travels at speed c in all inertial reference frames, regardless of how the reference frames are moving with respect to the light source. Relative to the spacecraft, the starlight is approaching at the speed of light c = 3.00 × 10 8 m/s.
37.7. Model: Assume the starship and the earth are inertial reference frames. Solve: It has been found that light travels at 3.00 × 10 8 m/s in every inertial frame, regardless of how the reference frames are moving with respect to each other. An observer on the earth will measure the laser beam’s speed as 3.00 × 10 8 m/s.

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37.8. Model: Assume the earth is an inertial reference frame. Solve: Light travels at speed c in all inertial reference frames, regardless of their motion with respect to the light source. The speed of each photon will be c in any such inertial reference frame.
37.9. Model: The clocks are in the same reference frame. Visualize: Solve: The speed of light is 300 m/ s 0.30 m/ns. c μ = = The distance from the origin to the point ( x, y, z ) = (30 m, 40 m, 0 m) is ( ) ( ) 2 2 30 m 40 m 50 m. + = So, the time taken by the light to travel 50 m is 50 m 167 ns 0.30 m/ns = The clock should be preset to 167 ns.

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37.10. Model: Bjorn and firecrackers 1 and 2 are in the same reference frame. Light from both firecrackers travels towards Bjorn at 300 m/ μ s. Visualize: Solve: Bjorn is 600 m from the origin. Light with a speed of 300 m/ μ s takes 2.0 μ s to reach Bjorn. Since this flash reaches Bjorn at t = 3.0 μ s, it left firecracker 1 at t 1 = 1.0 μ s. The flash from firecracker 2 takes 1.0 s μ to reach Bjorn. So, the light left firecracker 2 at t 2 = 2.0 μ s. Note that the two events are not simultaneous although Bjorn sees the events as occurring at the same time.
37.11. Model: Bianca and firecrackers 1 and 2 are in the same reference frame. Light from both firecrackers travels toward Bianca at 300 m/ μ s. Visualize: Solve: The flash from firecracker 1 takes 2.0 s μ to reach Bianca ( ) 600 m 300 m/ s μ ÷ . The firecracker exploded at t 1 = 1.0 μ s because it reached Bianca’s eye at 3.0 μ s. The flash from the firecracker 2 takes 1.0 s μ to reach Bianca. Since firecrackers 1 and 2 exploded simultaneously, the explosion occurs at t 2 = 1.0 μ s. So, the light from firecracker 2 reaches Bianca’s eye at 2.0 μ s. Although the events are simultaneous, Bianca sees them occurring at different times.

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37.12. Model: You and your assistant are in the same reference frame. Light from the two lightning bolts travels toward you and your assistant at 300 m/ μ s. You and your assistant have synchronized clocks. Visualize: Solve: Bolt 1 is 9.0 km away, so it takes 30 μ s for the light to reach you ( ) 9000 m 300 m/ s μ ÷ . Bolt 2 is 3.0 km away from you, so it takes 10 μ s to reach you. Since both flashes reach your eye at the same time, event 1 happened 20 μ s before event 2. If event 1 happened at time t 1 = 0 then event 2 happened at time t 2 = 20 μ s. For your assistant, it takes light from bolt 1 10 μ s
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