Carrie measures her spaceship to have a length of 100m. Peter measures Carrie’s spaceship to have a length of 91m.

(i) Explain why Carrie measures the proper length of the spaceship.

(ii) Show that Carrie travels at a speed of approximately 0.4 c relative to Peter.

According to Carrie, it takes the star ten years to reach her. Using your answer to (a)(ii), calculate the distance to the star as measured by Peter.

According to Peter, as Carrie passes the star she sends a radio signal. Determine the time, as measured by Carrie, for the message to reach Peter.

(i) proper length is measured by observer at rest relative to object / Carrie is at rest relative to spaceship;

(ii) \(\gamma  = \left( {\frac{{100}}{{91}} = } \right)1.1\);
evidence of algebraic manipulation e.g. \(\frac{{{v^2}}}{{{c^2}}} = 1 - \frac{1}{{{{1.1}^2}}}\) to give v=0.42c;
≈0.4c

travel time measured by Peter = (10×γ=)11years;
4.6ly or 4.4ly (if 0.4 c used);

moves away at 0.42 c so is 4.2ly away when signal emitted; (allow ECF from (a)(ii))
signal travel time t where ct=4.2+0.42ct;
7.2y or 7y (if 0.4 c used);