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Chapter 12: Q27P (page 535)

A cop pulls you over and asks what speed you were going. 鈥淲ell, officer, I cannot tell a lie: the speedometer read 4脳108m/s.鈥� He gives you a ticket, because the speed limit on this highway is 2.5脳108m/s . In court, your lawyer (who, luckily, has studied physics) points out that a car鈥檚 speedometer measures proper velocity, whereas the speed limit is ordinary velocity. Guilty, or innocent?

Short Answer

Expert verified

The driver is innocent.

Step by step solution

01

Expression for the relationship between proper velocity and ordinary velocity:

Write the relationship between proper and ordinary velocity.

u=11-畏2c2畏 鈥︹�� (1)

Here, 畏is the proper velocity, u is the ordinary velocity, and c is the speed of light.

02

Determine that the driver is guilty or innocent:

Substitute 4脳108m/sfor畏 and3脳108m/s forc in equation (1).

u-11-4脳108m/s23脳108m/s24脳108m/su-0.6脳4脳102m/su-2.4脳108m/s

As the ordinary velocity is less than the speed light u<s, the driver maintained his car鈥檚 speed, and hence lawyer proved him innocent.

Therefore, the driver is innocent.

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