regrine falcons frequently grab prey birds from the air. Sometimes they strike at high enough speeds that the force of the impact disables prey birds. A 480 g peregrine falcon high in the sky spies a 240 g pigeon some distance below. The falcon slows to a near stop, then goes into a dive--called a stoop--and picks up speed as she falls. The falcon reaches a vertical speed of 45 m/s before striking the pigeon, which we can assume is stationary. The falcon strikes the pigeon and grabs it in her talons. The collision between the birds lasts 0.015 s.

This part can be solved by the Conservation of linear momentum principle, which establishes the initial momentum [tex]p_{i}[/tex] before the collision must be equal to the final momentum [tex]p_{f}[/tex] after the collision:

[tex]p_{i}=p_{f}[/tex] (1)

Being:

[tex]p_{i}=MV_{i}+mU_{i}[/tex]

[tex]p_{f}=(M+m) V[/tex]

Where:

[tex]M=480 g \frac{1 kg}{1000 g}=0.48 kg[/tex] the mas of the peregrine falcon

[tex]V_{i}=45 m/s[/tex] the initial speed of the falcon

[tex]m=240 g \frac{1 kg}{1000 g}=0.24 kg[/tex] is the mass of the pigeon

[tex]U_{i}=0 m/s[/tex] the initial speed of the pigeon (at rest)

[tex]V[/tex] the final speed of the system falcon-pigeon

Then:

[tex]MV_{i}+mU_{i}=(M+m) V[/tex] (2)

Finding [tex]V[/tex]:

[tex]V=\frac{MV_{i}}{M+m}[/tex] (3)

[tex]V=\frac{(0.48 kg)(45 m/s)}{0.48 kg+0.24 kg}[/tex] (4)

[tex]V=30 m/s[/tex] (5) This is the final speed

b) Force on the pigeon

In this part we will use the following equation:

[tex]F=\frac{\Delta p}{\Delta t}[/tex] (6)

Where:

[tex]F[/tex] is the force exerted on the pigeon

[tex]\Delta t=0.015 s[/tex] is the time

[tex]\Delta p[/tex] is the pigeon's change in momentum

Then:

[tex]\Delta p=p_{f}-p_{i}=mV-mU_{i}[/tex] (7)

[tex]\Delta p=mV[/tex] (8) Since [tex]U_{i}=0[/tex]

Substituting (8) in (6):

[tex]F=\frac{mV}{\Delta t}[/tex] (9)

[tex]F=\frac{(0.24 kg)(30 m/s)}{0.015 s}[/tex] (10)

Finally:

[tex]F=480 N[/tex]