Question

1. Relativistic velocity addition: Consider a universe in which Einstein's postulates and special relativity are valid but the speed of light c 300 miles/hour. A Kia with proper length L and a Bugatti with proper length 2L are racing. The Kia moves at a fixed radar gun. In the Kia's reference frame, both cars have the same length. What is the speed VB of the Bugatti with respect to the radar gun? speed UK= c/4 with respect to a 3c cos (wt)/4 and 3c sin(wt)/4w, where w = 9.955 108s1, i.e. T/yr. The rocket will thus 2. Worldlines and aging: Suppose a rocket leaves Earth and has velocity v(t) hence position x(t) return to Earth exactly 1 year after leaving - in Earth's frame. How long does this trip take in the rocket frame?

Need help with these two problems. Thanks!

Answer 1

Bugatti kia tlari RL Vr 음 If a observer see the Bugatti from kia's reference frame he/she will see the Bugatti has longth L due to length Contraction. So from kia reference frame, 1- VBK We are - Yox = 0.86667 given that velocity of kia werit radar var = 4 hence the velocity of Blagalti wort rader Vor = VBK + "ko . It VBKY KÁ

Br= 0.866 ct 0.25c 1 + 0.86x0.25c? = 1.116 1+ 0.2165 Vher = 14116 x 3 ou 1.2165 Br = 275.215 miles/hol or = 0.9) 0.917 C I Br

given, V(H) = 3cces (wit) 1+1 = 3sin swt) 4 , w = 9.955 xifoºls 4w Proper time t = from time dilation Rocket's frame. 1 year = 3.15* lot sic. the time taken from = 3.15 x 17 v1- q ckos (91955 X 15% %3.15x10} 315 X t2 = 3:15 x 107 Vi - Cos (9.135) ? 3:15x107 . 016637 te = 47 592173.39448 or tre 1.5 yeary I fence tart