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Math Help - projectile motion

  1. #1
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    projectile motion

    Letís suppose you throw a ball straight up with an initial speed of 50 feet per second from a height of 6 feet.
    1. Find the parametric equations that describe the motion of the ball as a function of time.
    2. How long is the ball in the air?
    3. Determine when the ball is at maximum height. Find its maximum height.
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  2. #2
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    how far can you get?
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    I have all the answer correct until C. I cant figure out whether i need to factor, or simplify. I also know that the maximum height is the y coordinate of the vertex.
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  4. #4
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    There are two ways to get your maximum height:

    Method 1 (requires calculus)
    i assume you ahve a parametric equation for the vertical motion like: y=f(t)

    differentiate and find the value of t where \frac{dy}{dt} = 0. This will give you the time at which the ball is at its maximum height.
    The height at that moment is then f(t).


    Method 2
    Consider the vertical motion of the ball only and use one of Newton's equations of motion:

    v=u + at
    v = 0 (at maximum height, it is no longer gaining altitude)
    u = ? (should have been given in question)
    a = accelleration (you should know the value of this!)
    t = the time at which max height is reached (solve for this)

    Then use another equation to get the height at this moment, eg
    v^2 = u^2 + 2as
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  5. #5
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    Quote Originally Posted by kenzie103109 View Post
    Letís suppose you throw a ball straight up with an initial speed of 50 feet per second from a height of 6 feet.
    1. Find the parametric equations that describe the motion of the ball as a function of time.
    2. How long is the ball in the air?
    3. Determine when the ball is at maximum height. Find its maximum height.
    y = 6 + 50t - 32t^2

    set y = 0 and solve for t to determine how long the ball is airborne.

    the graph of y is parabolic ... use t = \frac{-b}{2a} to find the vertex (time of max height)
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