After hitting the tree, how far did the ball travel horizontally in the sky when Kaushik saw the ball?

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Solution

Q.
One evening, Kaushik was in a park where children were playing cricket. Birds were singing in a nearby tree that was 80 m tall. He observed a bird on the tree at an angle of elevation of $45 degree$ .

When a sixer was hit, the ball flew through the tree, scaring the bird away. 2 seconds later, Kaushik noticed that the bird was flying at the same height but at an angle of elevation of $30 degree$ . Meanwhile, the ball was also flying towards him at the same height with an angle of elevation of $60 degree$ .

Based on the above information, answer the following questions:

(ii) (b) After hitting the tree, how far did the ball travel horizontally in the sky when Kaushik saw the ball

1 $80 (1 - \frac{1}{\sqrt{3}}) m$

2 $80 (1 - \frac{2}{\sqrt{3}}) m$

3 $80 (1 + \frac{1}{\sqrt{3}}) m$

4 $80 (1 + \frac{- 1}{\sqrt{3}}) m$

Ans.
(1)

$I n ∆ C G F t a n 60 ° = \frac{F G}{C G} \sqrt{3} = \frac{80}{C G} \Rightarrow C G = \frac{80}{\sqrt{3}} D i s \tan c e t h e b a l l t r a v e l l e d a f t e r h i t t i n g t h e t r e e : F A = G B = C B - C G = 80 - \frac{80}{\sqrt{3}} = 80 (1 - \frac{1}{\sqrt{3}}) m$

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