Question

a bird is sitting on  the top of the tree which is 80 m high. the angle of elevation of the bird from a point on the ground is 45 degree . the bird flies away from the point of observation horizontally and remains at constant height. after 2 seconds ,the angle of elevation of bird from point of observation becomes 30 degree. find the speed of bird.

Answer 1

let the bird's original position be C, the point on the ground directly below it B, and the observer's position A. the bird's new position D and the point directly below it E.

therefore:
<BAC = 45°
<DAE = 30°
BC = DE = 80m

in ∆ABC,
as cot 45° = 1
therefore AC/BC = 1
AC/80 = 1
AC = 80m ___ (i)

in ∆ADE,
as tan 30° = 1/√3
therefore DE/AE = 1/√3
80/AE = 1/√3
AE = 80√3 ___ (ii)

from (i) and (ii):
DB = EC = AE - AC = 80√3 - 80
= 80(√3-1)
= 80(1.732-1)
= 80 * 0.732
= 58.56 m

speed of bird = distance/time
= 58.56/2
= 29.28 m/s