# YouÂ areÂ workingÂ forÂ theÂ DefendersÂ ofÂ WildlifeÂ onÂ theÂ protectionÂ ofÂ theÂ baldÂ eagle,Â anÂ endangeredÂ species.Â WaltÂ DisneyÂ Productions,Â Inc.Â hasÂ agreedÂ toÂ helpÂ yourÂ causeÂ byÂ...

YouÂ areÂ workingÂ forÂ theÂ DefendersÂ ofÂ WildlifeÂ onÂ theÂ protectionÂ ofÂ theÂ baldÂ eagle,Â anÂ endangeredÂ species.Â WaltÂ DisneyÂ Productions,Â Inc.Â hasÂ agreedÂ toÂ helpÂ yourÂ causeÂ byÂ producingÂ anÂ animatedÂ movieÂ aboutÂ theÂ baldÂ eagle.Â YouÂ haveÂ setÂ upÂ aÂ dramaticÂ sceneÂ inwhichÂ aÂ youngÂ rabbitÂ isÂ frightenedÂ byÂ theÂ shadowÂ ofÂ theÂ eagleÂ andÂ startsÂ boundingÂ towardÂ theÂ eastÂ atÂ 30Â m/sÂ asÂ theÂ eagleÂ swoopsÂ downÂ verticallyÂ atÂ aÂ speedÂ ofÂ 15Â m/s.Â AÂ momentÂ beforeÂ theÂ eagleÂ contactsÂ theÂ rabbit,Â itÂ boundsÂ offÂ aÂ cliffÂ andÂ isÂ capturedÂ inÂ mid

air.Â TheÂ animatorsÂ wantÂ toÂ knowÂ howÂ toÂ portrayÂ whatÂ happensÂ justÂ afterÂ theÂ capture.Â IfÂ theÂ eagleÂ hasÂ aÂ massÂ ofÂ 2.5Â kgÂ andÂ theÂ rabbitÂ hasÂ aÂ massÂ ofÂ 0.8Â kgÂ whatÂ isÂ theÂ velocityÂ ofÂ theÂ eagleÂ withÂ theÂ rabbitÂ inÂ itsÂ talonsÂ justÂ afterÂ theÂ capture?Â Hint:Â YouÂ needÂ toÂ specifyÂ theÂ speedÂ andÂ directionÂ ofÂ theÂ eagle-rabbitÂ system.Â IncludeÂ aÂ diagramÂ ofÂ theÂ situationÂ beforeÂ andÂ afterÂ captureÂ withÂ vectorsÂ showingÂ theÂ initialÂ andÂ finalÂ velocities.

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Hey, let's try a conservation of momentum equation.Â As in:

Â Â Â Â Â BeforeÂ Â Â Â Â =Â Â Â Â Â after

m1v1 + m2v2 = m1v1 + m2v2

But, since this would be in angles, we need to have conservation of momentum in the x direction and the y direction.Â So, first, in the x direction.

We know all the masses and the velocities before collosion.Â We also know that the velocity after collision will be the same.Â Therefore, for the x direction (where the speed of the eagle would be 0):

0.8*30 + 2.5*0 = (0.8+2.5)v

24 = 3.3v

vx = 7.27 in the x direction

Now, we do the same for the y direction (where the speed of the rabbit is 0):

0.8*0 + 2.5*15 = (0.8+2.5)v

37.5 = 3.3v

vy = 11.36 in the y direction downward

The resultant velocity would be:

v = sqrt(vx^2 + vy^2)

v = sqrt(7.27^2 + 11.36^2) = 13.49.

For the angle, we use the velocities and the tangent function, as diagrammed in the image:

tan theta = 11.36/7.27

Theta = tan^(-1) (11.36/7.27) = 57.38 degrees below the horizontal.

Oops, here's the image.