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A law enforcement officer in an intergalactic "police car" turns on a red flashing light and sees it generate a flash every 1.2 s. A person on earth measures that the time between flashes is 2.2 s. How fast is the "police car" moving relative to the earth?

User Aumo
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1 Answer

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Answer:

The velocity of the police car relative to earth is
v_(rel) = 2.51* 10^(8) m/s

Given:

time for flash generation of the inter galactic police car, t = 1.2 s

time between flashes as measured from earth, t' = 2.2 s

Solution:

Utilising Einstein's equation for time dilation to calculate the velocity of the police car, the equation is given by:


t' = \frac{t}{\sqrt {1 - (v^(2))/(c^(2))}} (1)

where, c = speed of light in vacuum =
c = 3* 10^(8)

re arranging eqn (1) for velocity, v:


v_(rel) = c* \sqrt {1 - ((t)/(t'))^(2)} (2)

Now, from eqn (2)


v_(rel) = 3* 10^(8)( \sqrt {1 - ((1.2)/(2.2))^(2)})


v_(rel) = 3* 10^(8)* 0.838


v_(rel) = 2.51* 10^(8) m/s

User Jonsb
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