You are stationary on the ground and are watching a bird fly horizontally towards you at a rate of 2 m/s. The bird is located 20

Question

2 years ago

15

m above your head. How fast does the angle of elevation of your head change when the horizontal distance between you and the bird is 110 m

1 answer:

Ira Lisetskai [31] · Answer 1 · 2023-03-08T17:41:14+03:00

The angle of elevation changes by 0.0032 rad / sec

Let x (t) be the horizontal distance from you to bird.

Let θ be the angle of elevation of your head.

Then .tan θ = 20 /x

Differentiating

Sec² = dθ / dt = -20/x².dx/dt

dθ / dt = -20/x².dx/dt.cos²θ

dx/dt = -2m/s x = 110m

cos²θ = 110²/ (110²) + (20²) = 12100/12500

dθ / dt = 20/ (110)² x (-2) . 12100/12500

= 20 x 2/12500 = 0.0032 radian/s.

Hence ,

The angle of elevation changes by 0.0032 rad / sec

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