Question

If a 600g Falcon flies vertically downward at 20 m/s into a 1.5kg bird flying at 9m/s horizontally, and the impact is perpendicular to the direction the other bird is flying, by what angle did the falcon change the other birds direction of motion? Give angle measured from the horizontal. Assume the birds stick together briefly after the collision.

Answer 1

Using momentum conservation

In vertical direction

Pix = Pfx

m1*v1x + m2*v2x = M*Vx

m1 = mass of pigeon = 1.5 kg

m2 = mass of falcon = 600 gm = 0.6 kg

v1x = 9 m/sec

v2x = 0 m/sec (since initially falcon is moving straight downward)

Vx = V*cos A

M = 1.5 + 0.6 = 2.1 kg

So

1.5*9 + 0.6*0 = 2.1*V*cos A

V*cos A = 1.5*9/2.1 = 6.43 m/sec

Now momentum conservation in vertical direction

Piy = Pfy

m1*v1y + m2*v2y = M*V*sin A

v1y = 0 m/sec

v2y = initial speed of falcon = v2 = 20 m/sec

So,

1.5*0 + 0.6*20 = 2.1*V*sin A

V*sin A = 12/2.1 = 5.71

V*cos A = 6.43

divide above two equations:

tan A = 5.71/6.43 = 0.888

A = arctan (0.888) = 41.60 deg below the horizontal.

V = 6.43/cos 41.60 deg = 8.60 m/sec

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