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Chapter 6: Q6E (page 1247)

As you pilot your space utility vehicle at a constant speed toward the moon, a race pilot flies past you in her space racer at a constant speed of 0.800c relative to you. At the instant the space racer passes you, both of you start timers at zero. (a) At the instant when you measure that the space racer has travelled1.2脳108m past you, what does the race pilot read on her timer? (b) When the race pilot reads the value calculated in part (a) on her timer, what does she measure to be your distance from her? (c) At the instant when the race pilot reads the value calculated in part (a) on her timer, what do you read on yours?

Short Answer

Expert verified

a) t=0.3sb) =7.2脳107mc)t=0.3 s

Step by step solution

01

Concept of the time dilation equation.

The time dilation equation is given as螖迟=纬螖迟0/1-u2/c2 where鈭�t0 is the proper time in the rest frame,鈭�tis the time interval measured in the second frame of reference u is the speed of the second frame with respect to the rest frame, c is the speed of light

02

Calculate the time measured by the space racer

The proper time is the time measured by the space racer

螖t=d0.800c=1.2脳108m0.8脳3脳108=0.5s

纬=11-u2c2鈭�t0鈭�t0=11-u2c2鈭�t=11-0.8c2c2脳0.5=0.3s

Therefore, the proper time is 0.3s

03

STEP 3 Calculate the time when the race pilot reads the value calculated in part (a) on her time

d=鈭�t0脳0.800c=0.3脳0.8脳3脳108=7.2脳107m1.2脳108m0.8脳3脳108=0.5s

Therefore, t= 0.5 s

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Most popular questions from this chapter

Human skin is relatively insensitive to visible light, but ultraviolet radiation can cause severe burns. Does this have anything to do with photon energies? Explain.

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Space pilot Mavis zips past Stanley at a constant speed relative to him of 0.800c. Mavis and Stanley start timers at zero when the front of Mavis鈥檚 ship is directly above Stanley. When Mavis reads 5.00 s on her timer, she turns on a bright light under the front of her spaceship. (a) Use the Lorentz coordinate transformation derived in Example 37.6 to calculate x and t as measured by Stanley for the event of turning on the light. (b) Use the time dilation formula, Eq. (37.6), to calculate the time interval between the two events (the front of the spaceship passing overhead and turning on the light) as measured by Stanley. Compare to the value off you calculated in part (a). (c) Multiply the time interval by Mavis鈥檚 speed, both as measured by Stanley, to calculate the distance she has traveled as measured by him when the light turns on. Compare to the value of x you calculated in part (a).
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