Viewed by Carl: - Bob moves towards right at v = +0.98 c in his 10 m long spaces

ID: 1613378 • Letter: V

Question

Viewed by Carl:

- Bob moves towards right at v = +0.98 c in his 10 m long spaceship. He wears a clock that blinks every 10 seconds.

- Anna stands next to Carl in her 20 m long spaceship, and doesn’t move. She wears a clock that blinks every 10 seconds, too.

a. What is the length of Bob’s spaceship, when measured by Anna?

b. What is the length of Anna’s spaceship when measured by Bob?

c. What is the time interval between two blinks of Bob’s clock, when measured by Carl?

d. What is the time interval between two blinks of Anna’s clock, when measured by Bob?

e. What is the time interval between two blinks of Anna’s clock, when measured by Carl?

let

v = 0.98*c

L_B = 10 m, L_A = 20 m

a) the length of Bob’s spaceship, when measured by Anna L_B' = L_B*sqrt(1 - (v/c)^2)

= 10*sqrt(1 - 0.98^2)

= 1.99 m

b) the length of Anna’s spaceship when measured by Bob, L_A' = L_A*sqrt(1 - (v/c)^2)

= 20*sqrt(1 - 0.98^2)

= 3.98 m

c) the time interval between two blinks of Bob’s clock, when measured by Carl,

delta_t' = delta_t/sqrt(1 - (v/c)^2)

= 10/sqrt(1 - 0.98^2)

= 50.3 s

d) the time interval between two blinks of Anna’s clock, when measured by Bob,

delta_t' = delta_t/sqrt(1 - (v/c)^2)

= 10/sqrt(1 - 0.98^2)

= 50.3 s

e) delta_t = 10 s

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