To protect their young in the nest, peregrine falcons will fly into birds of pre

Question

To protect their young in the nest, peregrine falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a 600 g falcon flying at 20.0 m/s ran into a 1.50 kg raven flying at 9.00 m/s . The falcon hit the raven at a right angle to its original path and bounced back with a speed of 5.00 m/s . By what angle did the falcon change the raven's direction of motion?

Part C

Write down the initial x and y components of the momentum of the falcon: pFi,x and pFi,y. Then, write the initial x and y components of the momentum of the raven: pRi,x and pRi,y. Note that the initial components of momentum are the components of momentum before the collision.

Express your answers pFi,x, pFi,y, pRi,x, and pRi,y in this specific order and separated by commas, in kilogram meters per second.

Part D

Give the final x and y components of the momentum of the falcon: pFf,x and pFf,y. Note that the final components of momentum are the components of momentum after the collision.

Express your answers pFf,x and pFf,y separated by commas in kilogram meters per second.

Part E

Give the final x and y components of the momentum of the raven: pRf,x and pRf,y. Note that the final components of momentum are the components of momentum after the collision.

Since these quantities are unknown, you will need to use symbols to express the unknown terms. In particular, use the symbol ? for the angle between the raven's direction of motion after the collision and the positive x axis, and vRf for the raven's final speed.

Express your answers pRf,x and pRf,y separated by commas using the variables ?, for the angle that the raven's direction of motion makes with the positive x axis, and vRf, for the raven's final speed.

Part F

Which of the following statements correctly applies to the system that you are analyzing?

E) None of the components of total momentum are conserved because gravity acts on the system and the system is not isolated.

Part G

By what angle ? did the falcon change the raven's direction of motion?

Express your answer in degrees to two significant figures.

Part H

Despite being only about one-third the mass of the raven, the falcon successfully diverts the raven's direction of motion by a relatively large angle. This is because of the initial high speed of the falcon. In fact, by what angle ? would the falcon change the raven's direction of motion if it were to hit the raven at a lower speed, for example at a speed equal to the raven's initial speed? Assume that the raven has the same final speed as above and the falcon has the same final velocity as given in the introduction.

Express your answer in degrees to two sigificant figures.

A) Only the x component of total momentum is conserved, and one can write the following expression: pFi,x+pRi,x=pFf,x+pRf,x. B) Only the y component of total momentum is conserved, and one can write the following expression: pFi,y+pRi,y=pFf,y+pRf,y. C) Both the x and the y components of total momentum are conserved, and one can write the following expression: pFi,x+pRi,x+pFi,y+pRi,y=pFf,x+pRf,x+pFf,y+pRf,y. D) Both the x and the y components of total momentum are conserved, and one can write the following expressions: pFi,x+pRi,x=pFf,x+pRf,x and pFi,y+pRi,y=pFf,y+pRf,y.

E) None of the components of total momentum are conserved because gravity acts on the system and the system is not isolated.

Part G

By what angle ? did the falcon change the raven's direction of motion?

Express your answer in degrees to two significant figures.

Part H

Despite being only about one-third the mass of the raven, the falcon successfully diverts the raven's direction of motion by a relatively large angle. This is because of the initial high speed of the falcon. In fact, by what angle ? would the falcon change the raven's direction of motion if it were to hit the raven at a lower speed, for example at a speed equal to the raven's initial speed? Assume that the raven has the same final speed as above and the falcon has the same final velocity as given in the introduction.

Express your answer in degrees to two sigificant figures.

Explanation / Answer

Let's use an (x, y) coordinate system where positive x represents the raven's initial direction and positive y represents the falcon's initial direction. The we can describe the falcon's initial velocity as
.. vf1 = (0, 20) m/s
and the raven's initial velocity as
.. vr1 = (9, 0) m/s
The total initial momentum of the two birds combined is
.. mv1 = (0.60 kg)(0, 20) m/s + (1.5 kg)(9, 0) m/s
.. = (0, 12) kg•m/s + (13.5, 0) kg•m/s
.. = (13.5, 12) kg•m/s

After the collision, the falcon has a momentum of
.. mvf2 = (0.6 kg)(0, -5) m/s = (0, -3) kg•m/s

If momentum is conserved, then the raven will have this momentum after the collision:
.. mvr2 = mv1 - mvf2
.. = (13.5, 12) kg•m/s - (0, -3) kg•m/s
.. = (13.5, 15) kg•m/s

The angle with respect to the initial path is
.. angle = arctan(15/13.5) 48.0°

The components of the raven's final velocity are found be dividing momentum by mass:
.. vr2 = mvr2/(1.5 kg) = (9, 10) m/s
The magnitude of the raven's velocity is found using the Pythagorean theorem.
.. |vr2| = (9^2+10^2) m/s = 181 m/s 13.45 m/s

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