A person travels by a car at a speed of `180 kmh^(-1)` . It takes exactly 10 hours by his wristwatch to go from the station A to the station B . (a) What is the rest distance between the two stations ? (b) How much is taken in the road frame by the car to go from the station A to the station B?

Explanation

Given ` v = 180 km / hr = 50m/s `
`t = 10 hrs`.
Let the rest distance be L
` .: L' = (sqrt 1 -v^(2) / c^(2)) `
and `L' = 10 xx 180 = 1800 km `
` 1800 = L (sqrt (1-) ((180)^(2)) / (3 xx 10^(8))^(2))`
or, `L = (sqrt (3.24 xx 10^(6) ) / 1 - 36 xx 10^(-14)`
` = 1800 + 25 xx 10^(-12)`
or, 25 nm more than 1800 km
(b) Time takes by the car to cover the distance of road frame
` = 1.8 xx 10^(6) + 25 xx 10^(-9) / 50 `
` = 0.36 xx 10^(5) + 5 xx 10^(-8)`
` = 10 hours + 0.5 ns `