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Thread: velocity algebra help

  1. #1
    Junior Member
    Mar 2008

    velocity algebra help

    if a ball is thrown directly upward into the air with a velocity of 40 ft/sec, it's height (in feet) after t seconds is given by a the formula y=20+40t-16t^2. What is the maximum height attained by the ball?
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  2. #2
    o_O is offline
    Primero Espada
    o_O's Avatar
    Mar 2008
    The ball will reach its maximum height when the ball's velocity is equal to 0 (slowed down due to the force of gravity). So, using some kinematics:
    $\displaystyle v_{f} = v_{i} + at$
    $\displaystyle 0 = 40 + (-32.17)t$
    where a is the acceleration due to gravity in feet/sec^2

    Solve for t and plug into your original equation.

    Or if you know your mechanics and a bit of calculus, differentiate both sides and solve for t when $\displaystyle \frac{dy}{dt} = 0$ (i.e. when velocity is equal to 0)
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