Question

A car with a proper length of 8.0 m passes by. Calculate the contracted length when the speed of the car is 0.89c.

Answer 1

3.65 m

Step-by-step explanation

Given:

• The proper length of the car, L₀ = 8.0 m

,

• The speed of the car, v = 0.89c

Find:

• The contracted length of the car, L

The length contraction of an object, which is the shortening of the actual length of the object when it is moving relative to the observer's frame, is given by the equation,

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

Replace the known values and solve,

`L=8.0m\cdot\sqrt{1-((0.89c)^2)/(c^2)}=8.0m\cdot\sqrt{1-(0.89^2c^2)/(c^2)}=8.0m\cdot√(1-0.89^2)\approx3.65m`

Hence, the contracted length of the car is 3.65 m, rounded to the nearest hundredth.