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11 May, 13:49

A wildlife researcher is tracking a flock of geese. the geese fly 3.5 km due west, then turn toward the north by 40 ∘ and fly another 4.5 km, what is the magnitude of their displacement

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  1. 11 May, 15:48
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    To solve this problem, we can use the cosine formula for calculating the length of the displacement:

    c^2 = a^2 + b^2 - 2 a b cos θ

    where c is the displacement, a = 3.5 km, b = 4.5 km, and θ is the angle inside the triangle

    Since the geeze turned 40° from west to north, so the angle inside the triangle must be:

    θ = 180 - 40 = 140°

    c^2 = 3.5^2 + 4.5^2 - 2 (3.5) (4.5) cos 140

    c^2 = 56.63

    c = 7.53 km

    So the magnitude of the displacement is 7.53 km
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