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 hit a 1.50-kg raven flying at 9.0 m/s. The falcon hit the raven at right angles to its original path and bounced back at 5.0 m/s. (These figures were estimated by the author as he watched this attack occur in northern New Mexico.) By what angle did the falcon change the raven's direction of motion?

Accepted Answer

Convert the masses of the falcon and the raven into kilograms for consistency in SI units. The falcon's mass is 600 g, which is equivalent to 0.600 kg. The raven's mass is already given as 1.50 kg. Apply the principle of conservation of momentum. Since the collision occurs in two dimensions, break the momentum into x and y components. Write the momentum conservation equations for both components:

For the x-direction: 
$$m_{f}v$$_{f,x} + $$m_{r}v$$_{r,x} = $$m_{f}v$$_{f,x'} + $$m_{r}v$$_{r,x'}

For the y-direction: 
$$m_{f}v$$_{f,y} + $$m_{r}v$$_{r,y} = $$m_{f}v$$_{f,y'} + $$m_{r}v$$_{r,y'} Substitute the known values into the momentum conservation equations. For the initial velocities: 
- The falcon's initial velocity is 20.0 m/s in the x-direction, so v_{f,x} = 20.0 m/s and v_{f,y} = 0.
- The raven's initial velocity is 9.0 m/s in the y-direction, so v_{r,x} = 0 and v_{r,y} = 9.0 m/s.
- After the collision, the falcon's velocity is 5.0 m/s in the negative x-direction, so v_{f,x'} = -5.0 m/s and v_{f,y'} = 0. Solve the momentum conservation equations for the raven's final velocity components (v_{r,x'} and v_{r,y'}). Use the equations derived in step 2 and the substituted values from step 3. This will give you the x and y components of the raven's final velocity. Determine the angle by which the raven's direction of motion changes. Use the arctangent function to calculate the angle: 
θ = $$tan^{-1}(v$$_{r,y'} / v_{r,x'}). Ensure that you account for the correct quadrant based on the signs of v_{r,x'} and v_{r,y'}.

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Key Concepts

Momentum Conservation

Vector Components

Collision Angles