Question

A bird is sitting on the top of a 80m high tree.From a point on the ground ,the angle of elevation of the bird is 45 degrees.the bird flies away horizontally in such a way that it remained at a constant height from the ground.After 2 secs the angle of elevation of the bird from the same point is 30 degrees.find the speed of flying of the bird

Answer 1

First, it helps to draw a diagram.

The angle of elevation is the angle between the horizontal path of the bird and the line from the bird to the observer.

Because distance is equal to speed multiplied by time, we must find the distance (x) the bird traveled by using the angles.

By using the trigonometric relationships, we can find x with tangent.

So tan(30)=80m/x and solve for x. x=0.0072 m which is 7.2 mm.

Now that the distance is know, we can solve for speed. So D=ST, 0.0072m=S(2s).

Solving for S you get S=0.0036 m/s or 3.6 mm/s.