The mass of a pigeon hawk is twice that of the pigeons it hunts. Suppose a pigeo

Question

The mass of a pigeon hawk is twice that of the pigeons it hunts. Suppose a pigeon is gliding north at a speed of Vp = 23.0 m/s when a hawk swoops down, grabs the pigeon, and flies off. The hawk was flying north at speed of Vh = 34.0 m/s, at an angle = 45.0° below the horizontal, at the instant of the attack.

1) Find the final velocity of the birds just after the attack. (Express your answer to three significant figures.)

2)Find the final direction of the velocity vector of the birds just after the attack. (Express your answer to three significant figures.)

Explanation / Answer

Here ,

mass of pigeon = m

mass of hawk = 2 m

Vp = 23 j m/s

Vh = 34 m/s

theta = 45 degree

let the final velocity of the bird is v

Using conservation of momentum

m * Vp + 2 m * Vh = (m+ 2m) * v

23 j +2 * 34 * (cos(45) j + sin(45) k ) = 3 m * v

v = 23.7 j + 16.03 k

final velocity = sqrt(23.7^2 + 16.03^2)

final velocity = 28.61 m/s

the final velocity after the attack is 28.61 m/s

2)

direction of the velocity vector = arctan(16.03/23.7)

direction of the velocity vector = 34.1 degree

the direction of the velocity vector is 34.1 degree below horizontal

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