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?

A. 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.

B. 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.

C. 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.

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

Only the x component of total momentum is conserved, and one can write the following expression: pFi,x+pRi,x=pFf,x+pRf,x. Only the y component of total momentum is conserved, and one can write the following expression: pFi,y+pRi,y=pFf,y+pRf,y. 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. 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. None of the components of total momentum are conserved because gravity acts on the system and the system is not isolated.

Explanation / Answer

Let the Initial raven's direction be in the +x direction and the falcon in the + y direction.
m1 = 0.6 Kg
v1 = 20 i^ m/s

m2 = 1.5 Kg
v2 =  9.0 j^ m/s

A.)
pFi,x = m1 * v1 = 0.6 * 20 = 12 i^ kg m/s
pFi,y = m1 * 0

pRi,x = m2 * 0 = 0
pRi,y = m2 * v2 = 1.5 * 9 j^ = 13.5 j^ Kg m/s

B)
pFf,x = m1 * v1f = 0.6 * -5.0 i^ = - 3 i^ kg m/s
pFf,y = 0

C)
pRf,x = m2* vRf * cos() = 1.5*vRf * cos()
pRf,y = m2* vRf * sin() = 1.5*vRf * sin()

Using Momentum Conservation -
Initial Momentum = Final Momentum
Therefore
For X component -
pFi,x+pRi,x=pFf,x+pRf,x
12 kg m/s + 0 = -3 kg m/s + 1.5*vRf * cos()
vRf * cos() = 15/1.5
vRf * cos() = 10

For Y component -
pFi,y + pRi,y = pFf,y + pRf,y
0 + 13.5 kg m/s = 0 + 1.5*vRf * sin()
vRf * sin() = 13.5/1.5
vRf * sin() = 9


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.

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