To calculate the time interval as measured by the Vulcans when their ship has a speed of 0.940c with respect to Earth, we can use the time dilation formula from special relativity:
t' = t / sqrt(1 - v^2/c^2)
Where:
t' = time interval as measured by the Vulcans
t = time interval as measured on Earth (32.0 hours)
v = velocity of the Vulcan spacecraft (0.940c)
c = speed of light in a vacuum (3.00 x 10^8 m/s)
Plugging in the values:
t' = 32.0 / sqrt(1 - (0.940c)^2/c^2)
t' = 32.0 / sqrt(1 - 0.940^2)
t' = 32.0 / sqrt(1 - 0.8836)
t' = 32.0 / sqrt(0.1164)
t' = 32.0 / 0.341
t' = 93.85 hours
Therefore, the Vulcans would determine the time interval to be approximately 93.85 hours when their ship has a speed of 0.940c with respect to Earth.
A Vulcan spacecraft has a speed of 0.600c with respect to Earth. The Vulcans
determine 32.0 h to be the time interval between two events on Earth. What
value would they determine for this time interval if their ship had a speed of
0.940c with respect to Earth?
1 answer