Question

In order to get going fast, eagles will use a technique called stooping, in which they dive nearly straight down and tuck in their wings to reduce their surface area. While stooping, a 6-kg golden eagle can reach speeds of up to 53 m/s. While golden eagles are not very vocal, they sometimes make a weak, high-pitched sound. Suppose that while traveling at maximum speed, a golden eagle heads directly towards a pigeon while emitting a sound at 1.1 kHz. The emitted sound has a sound intensity level of 30 dB when heard at a distance of 5 m.

Part A: Not So Free Fallin’ Model this stooping golden eagle as an object moving at terminal velocity. The eagle’s drag coefficient is 0.5 and the density of air is 1.2 kg/m3 . What is the effective cross-sectional area of the eagle’s body while stooping?

Part B: The Doppler Effect What is the doppler-shifted frequency that the pigeon will hear coming from the eagle?

Part C: Dangerous Decibels? Consider the moment when the pigeon is 5 m away from the eagle. At the pigeon’s position, what is the intensity (in W/m 2 ) of the sound the eagle makes?

Part D: The Catch The golden eagle slams into the 250-g pigeon, which is initially moving at 10 m/s in the opposite direction (toward the eagle). The eagle grabs the pigeon in its talons, and they move off together in a perfectly inelastic collision. How fast do they move after the collision?

Thank you in advance for the help!

Answer 1

Part A)

At terminal velocity, net force on eagle is zero, the drag force on the eagle is equal to force of gravity.

Efffective cross-sectional area of eagle's body

Part B)

Frequency that the pigeon will hear is  

Part C)

Sound level

Intensity of sound eagle makes is

Part D)

Conserving momentum of pigeon and eagle before and after collision,

After collision, the bird's move with velocity