How Do Falcon Attacks Alter the Flight Path of Their Prey?

[mnafetsc]

Homework Statement

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 620 g falcon flying at 20.0 m/s hit a 1.40 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.)

A.By what angle did the falcon change the raven's direction of motion?
B.What was the raven's speed right after the collision?

Homework Equations

P=mv

conservation of momentum

The Attempt at a Solution

I put the falcon on the y-axis and the raven on the x axis, I ten tried to find the a and y components of p then did theta= arctan9p2/p1) which gave me 45 degrees-wrong

I then tried to find the x and y components using
m_F_v_Fi + m_R_V_Ri = m_F_v_Ff + m_R_V_Rf

Solving for v_Rf for the x and y compents I got 9 and 8.16 respectively, the had theta= arctan(8.16/9)= 42 degrees again wrong.

 

[HallsofIvy]

Homework Statement

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 620 g falcon flying at 20.0 m/s hit a 1.40 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.)

A.By what angle did the falcon change the raven's direction of motion?
B.What was the raven's speed right after the collision?

Homework Equations

P=mv

conservation of momentum

The Attempt at a Solution

I put the falcon on the y-axis and the raven on the x axis, I ten tried to find the a and y components of p then did theta= arctan9p2/p1) which gave me 45 degrees-wrong

Precisely how did you get that? Are you assuming a perfectly elastic collision? That's probably not correct. What percentage inelasticity are you assuming?

I then tried to find the x and y components using
m_F_v_Fi + m_R_V_Ri = m_F_v_Ff + m_R_V_Rf

Solving for v_Rf for the x and y compents I got 9 and 8.16 respectively, the had theta= arctan(8.16/9)= 42 degrees again wrong.

 

[mnafetsc]

Pretty much I did p=sqrt(p_1_^2 +p_2_^2

But I realize that is wrong because its not elastic situation, I know is inelastic, but not perfectly inelastic so I used the second equation thinking that would work, I'm not quite sure were to go from there.

 

[mnafetsc]

Never mind I was doing it correctly, I just kept making some unknown calculation error that kept giving me the wrong angle.

 

[rwisz]

I would approach this problem by first defining the variables and creating a diagram to visualize the situation. The variables in this problem are the masses of the falcon (m_F) and raven (m_R), their initial velocities (v_Fi and v_Ri), and their final velocities (v_Ff and v_Rf).

Next, I would use the conservation of momentum equation, which states that the total momentum before a collision is equal to the total momentum after the collision. In this case, since the falcon bounces back after the collision, its final momentum would be in the opposite direction and would have a negative sign.

Using this equation, I would set up the following:

m_Fv_Fi + m_Rv_Ri = -m_Fv_Ff + m_Rv_Rf

Since we are only concerned with the raven's motion after the collision, we can rearrange the equation to solve for v_Rf:

v_Rf = (m_Fv_Fi + m_Rv_Ri + m_Fv_Ff)/m_R

Substituting in the given values, we get:

v_Rf = (620 g x 20.0 m/s + 1.40 kg x 9.0 m/s + 620 g x 5.0 m/s)/(1.40 kg)

Simplifying, we get v_Rf = 11.4 m/s

This is the raven's speed right after the collision.

To find the angle at which the falcon changed the raven's direction of motion, we can use trigonometry. Since we know the initial and final velocities of the raven, we can use the inverse tangent function to find the angle:

θ = arctan(v_Rf/v_Ri)

Substituting in the values, we get:

θ = arctan(11.4 m/s/9.0 m/s)

Simplifying, we get θ = 51.3 degrees

Therefore, the falcon changed the raven's direction of motion by 51.3 degrees.

In conclusion, as a scientist, I would approach this problem by carefully defining the variables, using the conservation of momentum equation, and applying trigonometry to find the angle of change in direction and the raven's speed after the collision.