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13 July, 09:36

A tennis ball is thrown upward from the top of a 680 foot high building at a speed of 56 feet per second. The tennis ball's height above ground can be modeled by the equation. When does the tennis ball hit the ground?

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  1. 13 July, 09:43
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    t = 8.5 s

    Explanation:

    Kinematic equation of the movement of the tennis ball that is thrown upwards:

    y = y₀ + v₀*t - ½ g*t² Equation (1)

    Where:

    y : position of the ball as a function of time

    y₀ : Initial position of the ball

    t: time

    g: acceleration due to gravity in m/s²

    Known data

    g = 32 ft/s²

    y₀ = 680 ft

    v₀ = 56 ft/s

    Calculation of the time it takes for the ball to thit the ground

    We replace data en the equation (1)

    y = y₀ + v₀*t - ½ g*t²

    0 = 680 + (56) * t - ½ (32) * t²

    16*t² - (56) * t - 680 = 0 equation (2)

    solving equation (2) quadratic:

    t₁ = 8.5 s

    t₁ = - 5 s

    Time cannot be negative so the time it takes for the ball to hit the ground is t = 8.5 s
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