Q26 of 47 Page 1

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.

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


More from this chapter

All 47 →
24

In Fig. 8, O is the center of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle.

 25

Find x in terms of a, b and c:

 27

A thief runs with a uniform speed of 100 m/minute. After one minute a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.

 28

Prove that the area of a triangle with vertices is independent of t.