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 16.9 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 theta = 39.5degree below the horizontal, and a speed of 34.9 m/s. What is the speed of the eagle immediately after it catches its prey? Number m/s What is the magnitude of the angle, measured from horizontal, at which the eagle is flying immediately after the strike? Number degree

Explanation / Answer

Momentum is conserved during this collision.
The initial total momentum has components:
Px(initial) = m * 16.9 + 2m * 34.9 cos(-39.5)
Py(initial) = 2m *34.9 sin(-39.5)

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 * 16.9 + 2m * 34.9 cos(-39.5)

The mass drops out from both sides and so
Vx = 1/3 * ( 16.9 + 2* 34.9 cos(-39.5)) = 23.58 m/s

Likewise:

Vy = 1/3 * (2 * 34.9*sin(-39.5) ) = -14.8 m/s

So the speed is

V = sqrt(Vx^2 + Vy^2) = 27.84 m/s

The angle with the horizontal is:

tan(angle) = Vy/Vx = -14.8/23.58

angle = -32.12 degrees

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