College Calculus

If a ball is thrown vertically upward from the roof of 48 foot building with a velocity of 96 ft/sec, its height after t seconds is s(t)=48+96t−16t^2. What is the maximum height the ball reaches?

What is the velocity of the ball when it hits the ground (height 0)?

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  1. time in flight: solve s(t) = 0
    max height at the vertex: t=3
    v = 96-32t

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  2. the max height is on the axis of symmetry of the parabola
    ... t = -b / 2a ... -96 / (2 * -16)
    ... plug into the equation to find s

    velocity is ds/dt
    ... solve for t when s is zero
    ... plug into the 1st derivative of s(t)

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