The mass of a particular eagle is twice that of a hunted pigeon. Suppose the pig

Question

The mass of a particular eagle is twice that of a hunted pigeon. Suppose the pigeon is flying north at 17.3 m/s, when the eagle swoops down, grabs the pigeon, and flies off. At the instant right before the attack, the eagle is flying toward the pigeon at an angle 8-563° below the horizontal, and a speed of 40.1 m/s. What is the speed of the eagle immediately after it catches its prey? Number m/s 40.1 m/s What is the magnitude of the angle, measured from 17.3 m/s horizontal, at which the eagle is flying immediately after the strike? Number

Explanation / Answer

Momentum is conserved during this collision.
The initial total momentum has components:

Px(initial) = m * 17.3 + 2m * 40.1 cos(-56.3)
Py(initial) = 2m 40.1m/s sin(-56.3)

After the collision, the combination has mass 3m and

Px(after) = 3m Vx
Py(after) = 3m Vy

Because Px(after) = Px(initial) , we have

3m Vx = m * 17.3+ 2m * 40.1m/s cos(-56.3)

The mass drops out from both sides and so
Vx = 1/3 * ( 17.3 + 2* 40.1cos(-56.3)) = 30.89 m/s

Likewise:

Vy = 1/3 * (2 * 40.1*sin(-56.3) ) = -22.24 m/s

So the speed is

V = sqrt(Vx^2 + Vy^2) = 38.06 m/s

The angle with the horizontal is:

tan(angle) = Vy/Vx = -22.24/ 30.89

angle = -35.75 degrees

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