Question

A radar antenna is rotating and makes one revolution every 24 s, as measured on earth. However, instruments on a spaceship moving with respect to the earth at a speed v measure that the antenna makes one revolution every 44 s. What is the ratio v/c of the speed v to the speed c of light in a vacuum

Answer 1

Answer:

0.838

Explanation:

The ratio v/c of the speed v to the speed c of light in a vacuum is shown below:

Given that

$\triangle t_0 = 24\ seconds$ = time interval for one revolution

$\triangle t = 44\ seconds$ = time interval measured with speed v

based on the given information, the ratio v/c  of the speed v to the speed c of light in a vacuum is

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

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

Now squaring both the sides

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

Now remove the squaring root from both the sides and putting the values

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

$= {\sqrt{1 - \frac{(24)^2}{(44)^2}$

= 0.838