Question

An aeroplane flying horizontally $1$ km above the ground is observed at an elevation of ${60}^0$. If after $10$ secs the elevation is observed to be ${30}^0$. Then the uniform speed per hour the aeroplane is

• A. $20\sqrt{3}km$
• B. $240\sqrt{3}km$
• C. $256\sqrt{3}km$
• D. $250\sqrt{3}km$

Answer 1

The correct option is B $240\sqrt{3}km$

in $△AED$

$tan{60}^o=\frac{1}{ED}\Rightarrow ED=\frac{1}{\sqrt{3}}$

Similarly, in $△ABC$
$tan{30}^o=\frac{1}{EC}\Rightarrow EC=\sqrt{3}$

Distance travelled by aeroplane in 10 seconds $=EC-ED=\sqrt{3}-\frac{1}{\sqrt{3}}=\frac{2}{\sqrt{3}}$

$Speed=\frac{Distance}{Time}=\frac{\frac{2}{\sqrt{3}}}{\frac{10}{3600}}=240\sqrt{3}$

Therefore, Answer is $240\sqrt{3}$