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16 July, 08:08

Baseball player swings and hits a pop fly straight up in the air to the catcher. the height of the baseball in meters t seconds after it is hit is given by the quadratic function h left parenthesis t right parenthesis equals negative 4.9 t squared plus 34.3 t plus 1h (t) = â4.9t2+34.3t+1. how long does it take for the baseball to reach its maximumâ height? what is the maximum height obtained by theâ baseball?

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  1. 16 July, 08:38
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    The height at time t is given by

    h (t) = - 4.91t² + 34.3t + 1

    When the ball reaches maximum height, its derivative, h' (t) = 0.

    That is,

    -2 (4.91) t+34.3 = 0

    -9.82t + 34.3 = 0

    t = 3.4929 s

    Note that h'' (t) = - 9.82 (negative) which confirms that h will be maximum.

    The maximum height is

    hmax = - 4.91 (3.4929) ² + 34.3 (3.4929) + 1

    = 60.903 m

    Answer:

    The ball attains maximum height in 3.5 s (nearest tenth).

    The ball attains a maximum height of 60.9 m (nearest tenth)
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