Answer to Question #110334 in Quantum Mechanics for ROHIT SHARMA

Question

Inside a spacecraft travelling at a speed of 0.8c with respect to the earth, the time interval between two events on the earth is measured to be 30 hrs. What would the time interval be if the spacecraft was travelling at a speed of 0.9c.

Answer 1

Промежуток времени на космическом корабле $\Delta t_{01}=30hrs$ ,is related to the time span on Earth $\Delta t$  the formula

$\Delta t=\frac{\Delta t_{01}}{\sqrt{1-\frac{v_1^2}{c^2}}}$

define $\Delta t$

$\Delta t=\frac{30}{\sqrt{1-\frac{(0.8c)^2}{c^2}}}=\frac{30}{\sqrt{1-0.64}}=50 hrs$

then at speed $v_2=0.9c$ the space time on a spaceship is

$\Delta t_{02}= \Delta t_\cdot {\sqrt{1-\frac{v_2^2}{c^2}}}=50\cdot {\sqrt{1-\frac{(0.9c)^2}{c^2}}}=50\cdot {\sqrt{1-0.81}}=21.794 hrs=21 hrs 47 min 38.4 s$