Predicting A 2D Collision: You are working for the Defenders of Wildlife on the protection of the bald eagle, an endangered species. Walt Disney Productions, Inc. has agreed to help your cause by producing an animated movie about the bald eagle. You have set up a dramatic scene inwhich a young rabbit is frightened by the shadow of the eagle and starts bounding toward the east at 30 m/s as the eagle swoops down vertically at a speed of 15 m/s. A moment before the eagle contacts the rabbit, it bounds off a cliff and is captured in midair. The animators want to know how to portray what happens just after the capture. If the eagle has a mass of 2.5 kg and the rabbit has a mass of 0.8 kg what is the velocity of the eagle with the rabbit in its talons just after the capture? 

Hint: You need to specify the speed and direction of the eaglerabbit system. Include a diagram of the situation before and aftercapture with vectors showing the initial and final velocities.

Expert Answers

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

      Before      =      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.  So, first, in the x direction.

We know all the masses and the velocities before collosion.  We also know that the velocity after collision will be the same.  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.

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