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31 July, 04:01

A student takes his 2 dogs for a walk. He lets them off their leash in a field where Edison runs at 10 m/s and Einstein runs at 8 m/s. The student determines the angle between the dogs is 25°, how far are the dogs from each other in 5 seconds?

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  1. 31 July, 05:06
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    The dogs are 21. 8 m from each other in 5 seconds

    Step-by-step explanation:

    Given;

    speed of Edison, v = 10 m/s

    speed of Einstein, u = 8 m/s

    angle between the two dogs, θ = 25°

    let the distance ran by Edison in 5 seconds = x = (10 m/s x 5 s) = 50 m

    let the distance ran by Einstein in 5 seconds = y = (8 m/s x 5 s) = 40 m

    let the distance between the two dogs after 5 seconds = z

    x, y and z forms a triangle with an angle between x and y as θ

    The third side, z, can be calculated using cosine rule

    z² = x² + y² - 2xyCosθ

    z² = 50² + 40² - (2 x 50 x 40) Cos25

    z² = 4100 - 4000Cos25

    z² = 474.7689

    z = √474.7689

    z = 21.789 m ≅ 21. 8 m

    Therefore, the dogs are 21. 8 m from each other in 5 seconds
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