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 Ø=41.1° below the horizontal, and a speed of 37.3 m/s.

What is the speed of the eagle immediately after it catches it's prey?

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

Explanation / Answer

Here ,

let the vertical direction is y - axis ,

horizontal is x - axis

Now, velocity of pigeon ,

vp = 16.7 i m/s

velocity of eagle ,

ve = 37.3 *(cos(41.1) i - sin(41.1) j )

ve = 28.1 i - 24.5 j m/s

Now, let the final speed is v

using conservation of momentum ,

v*(m + 2m ) = m *(16.7 i ) + 2m (28.1 i - 24.5 j )

v = 24.3 i - 16.3 j m/s

Hence ,

speed = sqrt(24.3^2 + 16.3^2)

speed = 29.3 m/s

the speed of eagle is 29.3 m/s

angle = arctan(16.3/24.3)

angle = 33.9 degree

the angle is 33.9 degee below horizontal

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