If a ball is thrown vertically upward with a velocity of 160 ft/s, then its height after t seconds is s = 160t − 16t2. (a) What is the maxi

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If a ball is thrown vertically upward with a velocity of 160 ft/s, then its height after t seconds is s = 160t − 16t2. (a) What is the maximum height reached by the ball?

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Tài Đức 6 months 2021-08-18T07:39:12+00:00 1 Answers 13 views 0

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    2021-08-18T07:41:06+00:00

    Answer:

    s = 400 ft

    The maximum height reached by the ball is 400 ft

    Explanation:

    Given;

    Initial vertical velocity v = 160 ft/s

    Height function s = 160t – 16t^2 ……1

    The maximum height is reached when the change in height with respect to time is zero.

    ds/dt = 0

    Differentiating the height function;

    ds/dt = 160 – 32t = 0

    160 – 32t = 0

    Solving for t;

    32t = 160

    t = 160/32

    t = 5 seconds

    Therefore, the maximum height is at t = 5;

    Substituting into equation 1 (the height function)

    s = 160(5) – 16(5^2)

    s = 800 – 400

    s = 400 ft

    The maximum height reached by the ball is 400 ft

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