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# Find speed in Km/Hr ?

## Percy standing in the midst of a field observes a flying bird in his north at an angle of elevation of ${30}^{\circ}$ and after $2 \min$ he observes the bird in his south at an angle of elevation of ${60}^{\circ}$. If the birdflies in a straight line all along at a height of $50 \sqrt{3} m$, then find its speed in kilometer per hour.

Dec 11, 2017

$6 \textcolor{w h i t e}{88} k m {h}^{-} 1$

#### Explanation:

From the diagram we need to find distance c. Using Pythagoras' theorem $c = \sqrt{{a}^{2} + {b}^{2}}$. we first find a and b

$a = \frac{50 \sqrt{3}}{\sin} \left(30\right) = 100 \sqrt{3}$

$b = \frac{50 \sqrt{3}}{\sin} \left(60\right) = \frac{50 \sqrt{3}}{\frac{\sqrt{3}}{2}} = 100$

$c = \sqrt{{\left(100 \sqrt{3}\right)}^{2} + {\left(100\right)}^{2}}$

$c = \sqrt{40000} = 200 \textcolor{w h i t e}{88}$metres

$200 m = \frac{200}{1000} = \frac{1}{5} k m$

$2 \min = \frac{2}{60} = \frac{1}{30} h r s$

Distance travelled/ time taken = speed

$\therefore$

$\frac{\frac{1}{5}}{\frac{1}{30}} = 6$ $k m {h}^{-} 1$