Time dilation

Level 2

Clock A and B are exactly the same on earth. Now, clock B is on a space travel as in the picture. The spaceship is flying at a uniform velocity of $0.8$ c ( $80$ % of the velocity of light). Which of the following statements is correct?

a) When $6$ seconds passes on clock B, the observer watching the clock B through a telescope from earth will see $10$ seconds passing.

b) When $6$ seconds passes on clock A, the observer watching the clock A through a telescope from the spaceship will see $10$ seconds passing.

a) and b) b) only a) only none of them

1 solution

Jacopo Piccione
Sep 13, 2019

When two observers are in relative motion to each other, each will measure the other's clock slowing down, in concordance with them being moving relatively to the observer's frame of reference. Hence, using Time dilation formula:

$\Delta t_A=\frac{\Delta t_B}{\sqrt{1-(\frac{v_B}{c})^2}}=\frac{6}{\sqrt{1-0.8^2}}=10$

and also

$\Delta t_B=\frac{\Delta t_A}{\sqrt{1-(\frac{v_A}{c})^2}}=\frac{6}{\sqrt{1-0.8^2}}=10$

Time dilation

1 solution

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