Three birds are flying in a compact formation. The first bird, with a mass of 10

Question

Three birds are flying in a compact formation. The first bird, with a mass of 100 g is flying 35 degrees east of north t at a speed of 8 m/s. The second bird, with a mass of 123 g, is flying 2 degrees east of north at a speed of 11 m/s. The third bird, with a mass of 112 g, is flying 22 degrees west of north at a speed of 10 m/s. What is the momentum vector of the formation? What would be the speed and direction of a 115 g bird with the same momentum?

Include all formulas used and explain work clearly. Thanks!

Explanation / Answer

let i represent the axis west-east axis

j represent south-north axis

momentum of first bird = 100/1000*(8*sin35i + 8*cos35j) = 0.459i + 0.655j

momentum of second bird = 123/1000*(11*sin2i + 11*cos2j) = 0.0472i + 1.352j

momentun of third bird = 112/1000*(-10*sin22i + 10*cos22j) = -0.419i + 1.038j

total momentum of the system =(0.459i + 0.655j) + (0.0472i + 1.352j) + (-0.419i+1.038j)

momentum vector = 0.0872i + 3.045j

magnitude of total momentum = 3.046 kg.m/s

direction : = tan-1(0.0872/3.045) = 1.64 degrees
so,the total momentum is 1.64 degrees east of north
velocity of 115g bird v =3.046/(115/1000) = 26.49 m/s

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