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Math Help (URGENT X10)

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This is really urgent so please please please help.

The height(H) of an object that has been dropped or thrown in the air is given by:
t=time in seconds(s)
v=initial velocity in meters per second (m/s)
h=initial height in meters(m)

h=initial height
Is there a difference but, anyway I didn't make this clear on the last post.

A ball is thrown vertically upwardd from the top of the Leaning Tower of Pisa (height=53m) with an initial velocity of 30m/s. Find the time(s) at which:
a)the ball's height equals the hight of the tower

b)the ball's height is greater than the height of the tower

c)the ball's height is less than the height of the tower

d)the ball reaches its maximum height

I don't know how to do this problem.

Please Help and Thank You very much =)

  • Math Help (URGENT X10) - ,

    acceleration downward due to gravity is 10m/s to be exact 9.8m/s
    this is enough to get you to start thinking

  • Math Help (URGENT X10) - ,

    h(t) = -4.9t^2 + 30t + 53

    a) ball goes up, comes back down to the top of the tower. So, we want

    53 = -4.9t^2 + 30t + 53
    0 = -4.9t^2 + 30t
    0 = t(-4.9t + 30)
    so, t=0 (at the start) or t = 6.12 (as it comes back down)

    If t(-4.9t+30)=0, either
    -4.9t+30 = 0
    That is, t = 6.12

    If you can't solve a factored expression, you have some review to do.

    b) same calculation but, t is between 0 and 6.12. That is 0 < t < 6.12

    c) same calculation, but restricting t to positive values, t>6.12
    Naturally, we could also restrict t to the point where height >= 0.

    d) vertex of any parabola is where x = -b/2a = -30/-9.8 = 3.06

    you know from the quadratic formula that x = -b/2a ± sqrt(blah blah)
    Parabolas are symmetric, so the vertex is midway between the roots, which are equally spaced around x = -b/2a

    h(3.06) = 98.9

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