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30 August, 21:45

Tom kicks a soccer ball on a flat, level field with initial speed 20 m/s at an angle 35 degrees above the horizontal. (1) How long will the ball stay in the air (2) Max height will ball attain (3) How far away from tom will the ball land (4) what speed will the ball have in the instant just before it lands

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  1. 30 August, 22:42
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    Given:

    x₀ = 0 m

    y₀ = 0 m

    v₀ = 20 m/s

    θ = 35°

    aᵧ = - 9.8 m/s²

    1) Find t when y = 0.

    y = y₀ + v₀ᵧ t + ½ aᵧ t²

    0 = 0 + (20 sin 35°) t + ½ (-9.8) t²

    0 = t (20 sin 35° - 4.9 t)

    t = 0, t = 2.34

    The ball stays in the air 2.34 seconds.

    2) Find y when vᵧ = 0.

    vᵧ² = v₀ᵧ² + 2aᵧ (y - y₀)

    0² = (20 sin 35) ² + 2 (-9.8) (y - 0)

    y = 6.71 m

    The ball reaches a maximum height of 6.71 meters.

    3) Find x when y = 0.

    x = x₀ + v₀ₓ t + ½ aₓ t²

    x = 0 + (20 cos 35°) (2.34) + ½ (0) (2.3) ²

    x = 38.4 m

    The ball lands 38.4 meters from Tom.

    4) Find v when y = 0.

    vₓ = aₓ t + v₀ₓ

    vₓ = (0) (2.34) + 20 cos 35°

    vₓ = 16.4 m/s

    vᵧ = aᵧ t + v₀ᵧ

    vᵧ = (-9.8) (2.34) + 20 sin 35°

    vᵧ = - 11.5 m/s

    v = √ (vₓ² + vᵧ²)

    v = √ ((16.4) ² + (-11.5) ²)

    v = 20 m/s

    The ball has a speed of 20 m/s just before it lands.
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