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3 March, 09:38

Clay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at 45° with respect to the 50-yard line and covers 8.0 m in 1 s. He then runs straight down the field at 90° with respect to the 50-yard line for 12 m, with an elapsed time of 1.2 s. (a) What is Matthews' final displacement from the start of the play? (b) What is his average velocity?

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  1. 3 March, 09:54
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    a) D_ total = 18.54 m, b) v = 6.55 m / s

    Explanation:

    In this exercise we must find the displacement of the player.

    a) Let's start with the initial displacement, d = 8 m at a 45º angle, use trigonometry to find the components

    sin 45 = y₁ / d

    cos 45 = x₁ / d

    y₁ = d sin 45

    x₁ = d sin 45

    y₁ = 8 sin 45 = 5,657 m

    x₁ = 8 cos 45 = 5,657 m

    The second offset is d₂ = 12m at 90 of the 50 yard

    y₂ = 12 m

    x₂ = 0

    total displacement

    y_total = y₁ + y₂

    y_total = 5,657 + 12

    y_total = 17,657 m

    x_total = x₁ + x₂

    x_total = 5,657 + 0

    x_total = 5,657 m

    D_total = 17.657 i^ + 5.657 j^ m

    D_total = Ra (17.657 2 + 5.657 2)

    D_ total = 18.54 m

    b) the average speed is requested, which is the offset carried out in the time used

    v = Δx / Δt

    the distance traveled using the pythagorean theorem is

    r = √ (d1² + d2²)

    r = √ (8² + 12²)

    r = 14.42 m

    The time used for this shredding is

    t = t1 + t2

    t = 1 + 1.2

    t = 2.2 s

    let's calculate the average speed

    v = 14.42 / 2.2

    v = 6.55 m / s
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