Question

Example 1.1 A spacecraft is moving relative to the earth. An
observer on the earth finds that, between 1 p.m. and 2 p.m. accord-
ing to her clock, 3601 s elapse on the spacecraft's clock. What is the
spacecraft's speed relative to the earth?​

Answer 1

$hello \: mate$

Question : Example 1.1 A spacecraft is moving relative to the earth. An observer on the earth finds that, between 1 p.m. and 2 p.m. according to her clock, 3601 s elapse on the spacecraft's clock. What is the spacecraft's speed relative to the earth?

Answer :

Note :- Kindly refer the above attachment.

I hope my answer helps you.

Answer 2

The spacecraft's speed relative to the earth is  7.1 x 10⁶ m/s.

Here, $t_0$ = 3600s is the proper time interval on the earth.

t = 3601s is the time interval in the moving frame as measured from earth.

Thus,

            $t = \frac{t_0}{\sqrt{1 - \frac{v^2}{c^2} } }$

⇒     $1 - \frac{v^2}{c^2} = (\frac{t_0}{t} )^2$

⇒     $v = c\sqrt{1 - (\frac{t_0}{t} )^2}$

            $= (2.998 10^8 m/s) \sqrt{1- (\frac{3600 s}{3601 s} )^2}$

            = 7.1 x 10⁶ m/s

Thus the spacecraft's speed relative to the earth is  7.1 x 10⁶ m/s.

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