Two events in reference frame S occur 20 ? s apart at the same point in space. T

Question

Two events in reference frame S occur 20 ?s apart at the same point in space. The distance between the two events is 2600 m in reference frame S? .

Part A

What is the time interval between the events in reference frame S??

Part B

What is the velocity of S? relative to S?

Assignment38 Problem 36.48 Part A Problem 36.48 What is the time interval between the events in reference frame S'? Two events in reference frame S occur 20 us apart at he same point in space. The distance between the two ents is 2600 m in reference frame S = 18.66 Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining Part B What is the velocity of S' relative to S? What is the velocity of S relative to S? Submit My Answers Give Up

Explanation / Answer

a)

dx' = gamma (dx - v dt)

-2600 = gamma (0 - (v) (20e-6))

-2600 = 1/sqrt(1 - (v/(3e8))^2) (0 - (v) (20e-6))

2600 = 1/sqrt(1 - (v/(3e8))^2) ((v) (20e-6))

==> v = 1.1928 x 10^8 m/s

gamma is:

gamma = 1/sqrt(1 - (1.1928e8/(3e8))^2) = 1.0898

dt' = gamma (dt - v/c^2 dx)

dt' = (1.0898) (20 - v/c^2 (0))

dt' = 21.8 us

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b)

dx' = gamma (dx - v dt)

-2600 = gamma (0 - (v) (20e-6))

-2600 = 1/sqrt(1 - (v/(3e8))^2) (0 - (v) (20e-6))

2600 = 1/sqrt(1 - (v/(3e8))^2) ((v) (20e-6))

==> v = 1.1928 x 10^8 m/s

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