Question

An aeroplane travels over a rectangular field 100 m × 50 m, parallel to its length. What should be the speed of the plane so that the field becomes square in the plane frame?

Answer 1

Explanation:

It is observed that the rectangular field is a square when the length is equal to the breadth, that is, 50 m.

Contracted length is denoted as L‘, which is 50.

Original length is denoted as L, which is 100.

The aeroplane has the speed denoted as v.

Light’s velocity,$c=3 \times 10^{8} \mathrm{m} / \mathrm{s}$

It is known that $L^{\prime}=L 1-v 2 / c 2$

$\Rightarrow v=3 c 2=0.866 c$

⇒ v = 3c2 = 0.866c

So, the aeroplane’s speed must be equal to 0.866c, so that in the plane frame, the ground becomes square.

Answer 2

Answer:

Explanation:

* To make the field look square in the plane frame, either the breadth should increase or the length should decrease.

* Length Contraction will help us answer.

* The length of any object in a moving frame will appear foreshortened in the direction of motion, or contracted. The amount of contraction can be calculated from the Lorentz factor.

Adding an image from my Quora answer-