Question

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 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

Answer 1

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

Learn more about angle of elevation:brainly.com/question/16716174

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