# To reach her and light from bolt 2 30 μ s to reach

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to reach her and light from bolt 2 30 μ s to reach her. She sees the flash from bolt 1 at t = 10 μ s and the flash from bolt 2 at t = 50 μ s. That is, your assistant sees flash 2 40 μ s after she sees flash 1.

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37.13. 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 hits 9.0 km away, so the light takes 30 μ s to reach you (9000 m ÷ 300 m/ μ s). You see this flash at t = 50 μ s, so the lightning hit at t 1 = 20 μ s. Light from bolt 2, which hits 3.0 km away, takes 10 μ s to reach you. You see it at 10 μ s, so the lightning hit at t 2 = 0 μ s. The strikes are not simultaneous. Bolt 2 hits first, 20 μ s before bolt 1. Your assistant is in your inertial reference frame, so your assistant agrees that bolt 2 hits first, 20 μ s before bolt 1. Assess: A simple calculation would show that your assistant sees the flashes at the same time. When the flashes are seen is not the same as when the events happened.
37.14. Model: Light from the two lightning bolts travels toward Jose at 300 m/ μ s. Visualize: Solve: Bolt 1 light takes 1 s μ to reach Jose ( ) 300 m 300 m/ s . μ ÷ On the other hand, the flash from bolt 2 takes 3 μ s to reach him. The times when the flashes are seen are 1 seen 1 happened 1.0 s t t μ = + 2 seen 2 happened 3.0 s t t μ = + Because Jose sees the tree hit 1.0 μ s before he sees the barn hit, 2 seen 1 seen 1.0 s. t t μ = Subtracting the two equations, ( ) ( ) 2 seen 1 seen 2 happened 1 happened 3.0 s 1.0 s t t t t μ μ = + 1.0 μ s = ( ) 2 happened 1 happened t t + 2.0 μ s t 1 happened = t 2 happened + 1.0 μ s Thus, the barn was struck by lightning 1.0 μ s before the tree.

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37.15. Model: Your personal rocket craft is an inertial frame moving at 0.9 c relative to stars A and B. Solve: In your frame, star A is moving away from you and star B is moving toward you. When you are exactly halfway between them, both the stars explode simultaneously. The flashes from the two stars travel toward you with speed c . Because (i) you are at rest in your frame, (ii) the explosions are equally distant, and (iii) the light speed is c , independent of the fact that the stars are moving in your frame, the light will arrive simultaneously.
37.16. Model: The earth is in reference frame S and the cosmic ray is in reference frame S´. Frame S´ travels with velocity v relative to frame S. Solve: Two events are “cosmic ray enters the atmosphere” and “cosmic ray hits the ground.” These can both be measured with a single clock in the cosmic ray’s frame, frame S´, so the time interval between them in S´ is the proper time interval: t ´ = τ . The time interval measured in the earth’s frame, frame S, is t = 400 μ s. The time- dilation result is 2 1 t τ β Δ = Δ The cosmic ray’s speed in frame S is simply 8 6 60,000 m 1.5 10 m/s 0.50 400 10 s L v v t c β Δ = = = × = = Δ × Thus the time interval measured by the cosmic ray is 2 1 (0.50) (400 s) 346 s τ μ μ Δ = =

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37.17.
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