Question
An aeroplane travels over a rectangular field 100m × 50m, parallel to its length. What should be the speed of the plane so that the field becomes square in the plane frame?
✓
Answer
The rectangular field appears to be a square when the length becomes equal to the breadth i.e. 50m.
i.e. $\text{L}'=50;\ \text{L}=100 ;\ \text{v}={?}$
$\text{C} = 3 \times10^8\text{m/s}$
We know, $\text{L}'=\text{L}\sqrt{1-\frac{\text{v}^2}{\text{c}^2}}$
$\Rightarrow50=100\sqrt{1-\frac{\text{v}^2}{\text{c}^2}}$
$\Rightarrow\text{v}=\sqrt{\frac{3}{2\text{c}}}=0.866\text{c}$
i.e. $\text{L}'=50;\ \text{L}=100 ;\ \text{v}={?}$
$\text{C} = 3 \times10^8\text{m/s}$
We know, $\text{L}'=\text{L}\sqrt{1-\frac{\text{v}^2}{\text{c}^2}}$
$\Rightarrow50=100\sqrt{1-\frac{\text{v}^2}{\text{c}^2}}$
$\Rightarrow\text{v}=\sqrt{\frac{3}{2\text{c}}}=0.866\text{c}$
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