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

Thus the time interval will be 19.11 hrs.

Explanation:

Here length contraction will take place when we travel with speed comparable to speed of light

L = Lo  √ 1−  v^ 2 / c^2

L = Lo √ 1−  (0.81 c)^ 2 /  c^2  =Lo  × 0.6

t = L / v

t = 0.6 Lo / 0.8 c

Lo = 0.8 c x 30 hrs / 0.6 = 40 c.hrs

In the second case the speed is 0.9 c then

L = Lo √  1−  v^ 2 / c^2

L = Lo √ 1 −  (0.81 c)^ 2 /  c^2 = 0.43 Lo

t = L/v = 0.43 Lo / 0.9 c = 0.43 x  40 c.hrs/ 0.9 c

t = 19.11 hrs

Thus the time interval will be 19.11 hrs.