Q14 of 22 Page 9

A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Find the speed of flying of the bird.(CBSE 2016)

On the basis of condition given in the question the figure can be drawn as:


Let us assume BC be the tree and BD be x and AB be y


Now in right triangle ABC, we have



(i)


Also, in right triangle ADE we have





Now putting the value of y from (i), we get



∴


x = 80 (1.732 – 1)


= 80 × 0.732


= 58.56 m


We know that,


∴



= 29.28 m/sec

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