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 ? = 50.3° below the horizontal, and a speed of 41.1 m/s. Please answer the following two questions:

~What is the speed of the eagle immediately after it catches its prey?

~What is the magnitude of the angle, measured from horizontal, at which the eagle is flying immediately after the strike?

(Information and diagram below, and many thanks in advance.)

Explanation / Answer

momentum conservation of both eagle and pigeon

2m*41.1*cos(50.3) + m*17.3 = 3m*Vx ( in X direction)

2m*41.1*0.638 + m*17.3 = 3m*V

=> Vx = 23.24 m/s

2m*41.1*sin(50.3) = 3m*Vy

2m*41.1*0.769 = 3m*Vy

=> Vy = 21.07 m/s

V = sqrt (Vx^2 + Vy^2) = sqrt ( 23.24^2 + 21.07^2) = 31.36 m/s

theta = tan^-1( 21.07/23.24) = 42.17   measured from horizontal

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