Question

A kite is flying at a height of $60m$ above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is ${60}^o$. Find the length of the string assuming that there is no slack in the spring.

• A. $l=60\sqrt{2}m$
• B. $l=40\sqrt{2}m$
• C. $l=20\sqrt{2}m$
• D. None of these
  

Answer 1

The correct option is D None of these

$P$ is the position of the kite. Its height from the point $Q$ (on the ground)$=PQ=60m$

Let $OP=l$ be the length of the string

$\angle POQ={60}^o$ (given)

$sin\left(\Theta \right)=\frac{Opposite}{Hypotenuse}$

Now, $\frac{PQ}{OP}=\sin {60}^o$

$\Rightarrow$ $\frac{60}{l}=\sin {60}^o=\frac{\sqrt{3}}{2}$

$\Rightarrow$ $\frac{60}{l}=\frac{\sqrt{3}}{2}$

$\Rightarrow$ $l=\frac{3\times 2\times 20}{\sqrt{3}}m$

$\Rightarrow$ $l=40\sqrt{3}m$

The length of the string is $40\sqrt{3}m$