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Math Help - Ball thrown upwards

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    Ball thrown upwards

    A ball weighing .15kg is thrown upwards at a rate of 20m/s from a building 30m high. Neglecting air resistance, formulate a differential equation govering the ball's motion, solve it, and use the solution to determine the maximum height of the ball.
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    Quote Originally Posted by HelloWorld2 View Post
    A ball weighing .15kg is thrown upwards at a rate of 20m/s from a building 30m high. Neglecting air resistance, formulate a differential equation govering the ball's motion, solve it, and use the solution to determine the maximum height of the ball.
    Motion up: \displaystyle \frac{d^2 x}{dt^2} = -g subject to the boundary conditions that at t = 0, \displaystyle \frac{dx}{dt} = 20 and x = 0. (SI units used).
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    Quote Originally Posted by mr fantastic View Post
    Motion up: \displaystyle \frac{d^2 x}{dt^2} = -g subject to the boundary conditions that at t = 0, \displaystyle \frac{dx}{dt} = 20 and x = 0. (SI units used).
    This treats the top of the building as x = 0; in reference to the ground we can put x = 30.
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    So we just find an explicit expression for velocity, then integrate it, and apply the fact that s(0)=30 for the contstant. Then plug in the t that makes v=0?
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    Quote Originally Posted by HelloWorld2 View Post
    So we just find an explicit expression for velocity, then integrate it, and apply the fact that s(0)=30 for the contstant. Then plug in the t that makes v=0?
    Yes.
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