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 16.7 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 of theta= 48.7 degrees below the horizontal and a speed of 34.9 m/s.

a.) what is the speed of the eagle immediately after it catches the prey?

b) what is the magnitude of the angle, measured from horizonatl at which the eagle is flying immediately after the strike

Explanation / Answer

Given

mass of pigeion m , mass o f eagle is 2m

velocity of pigeion flying north is 16.7 m/s

eagle

the eagle is flying toward the pigeon at an angle of theta= 48.7 degrees

below the horizontal and a speed of 34.9 m/s.

here by considering the conservation of momentum

the components of momentum of pigeion and eagle before and after

before P_X = m*16.7+2m*34.9 cos(-48.7)

P_y = 0+2m*34.9 sin(-48.7)

after  

P_x = (m+2m)Vx

P_y = (m+2m) Vy

conservation of momentum then  

a)

(m+2m)Vx = m*16.7+2m*34.9 cos(-48.7)

Vx = (1/3) (16.7+2*34.9 cos(-48.7)) m/s = 20.92 m/s

Vy = (1/3)(2*34.9 sin(-48.7) )= -17.48 m/s

the magnitude is V = sqrt(Vx^2+Vy^2

V = sqrt(20.92^2+(-17.48)^2) m/s

V = 27.261m/s

b) The direction is  

tan theta = (Vy/Vx)

theta = arc tan (Vy/vx)

theta = arc tan (-20.92/17.48)

theta = -50.12 degrees

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