Question

A tourist is walking at a speed of 1.3 m/s along a 9.0-km path that follows an old canal. If the speed of light in a vacuum were 3.0 m/s, how long would the path be, according to the tourist?

Answer 1

The length is 8111.1 m.

Step-by-step explanation:

Given that,

Speed of tourist = 1.3 m/s

Distance = 9.0 km

Speed of light = 3.0 m/s

We need to calculate the length

Using formula of length

`L= L_(0)\sqrt{1-((v)/(c))^2}`

Where, l = length

`L_(0)`=original length

v = speed of tourist

c = speed of light

Put the value into the formula

`L=9000*\sqrt{1-((1.3)/(3.0))^2}`

`L=8111.1\ m`

Hence, The length is 8111.1 m.

Answer 2

The length of path according to the tourist is 8111.10 meters.

Step-by-step explanation:

It is given that,

Speed of tourist, v = 1.3 m/s

Path length, L₀ = 9 km = 9000 m

If the speed of light in a vacuum were 3.0 m/s. We need to find the length of path according to the tourist. Let it is L. It is a case of length contraction.

So,
`L=L_0\sqrt{1-(v^2)/(c^2)}`

`L=9000* \sqrt{1-((1.3)^2)/((3)^2)}`

L = 8111.10 m

So, the length of path according to the tourist is 8111.10 meters. Hence, this is the required solution.