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Motion in One Dimension

  1. Sep 18, 2009 #1
    I have a few problems I'm having trouble with. If I can get some help with this one I should be able to figure out the rest I have.

    1. A rock is thrown downward from the top of a tower with an initial speed of 12 m/s. If the rock hits the ground after 2.0 s, what is the height of the tower? (neglect air resistance).

    Known:
    [tex]Vi=12m/s[/tex]
    [tex]\Delta t=2 s[/tex]
    [tex]a=9.8 m/s[/tex]

    Relevant equations:
    [tex]Vf^2=Vi^2+2a(\Delta y)[/tex]



    My attempt:
    [tex]\Delta y=Vf^2-Vi^2-(2a)[/tex]
    [tex]\Delta y=0-144-(2*9.8 m/s^2)[/tex]
    [tex]\Delta y=-163.6[/tex]
    [tex]Height=163.6 m[/tex]

    I'm not sure if this is right. I think I run into trouble when I rearrange the formula. Multiple choice answer D is 63 m, so it's either a typo or I'm doing something wrong. A little guidance please? Thank you!
     
  2. jcsd
  3. Sep 18, 2009 #2

    rl.bhat

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    Homework Helper

    If a = b + gc, then
    c = (a - b)/g
    So your Δy formula is wrong.
     
  4. Sep 18, 2009 #3
    Ah, ok. I see what I did.

    Corrected formula:
    [tex]\Delta y=Vf^2-Vi^2/2a[/tex]


    I also need to first find the final velocity:

    [tex]Vf=Vi+a(\Delta t)[/tex]
    [tex]Vf=12 m/s + 9.8 m/s^2 (2 s)[/tex]
    [tex]Vf=31.6 m/s[/tex]

    Now for [tex]\Delta y[/tex]:

    [tex]\Delta y = (31.6m/s^2) - (12 m/s^2) / 2(9.8m/s^2)[/tex]:
    [tex]\Delta y = 43.6 m[/tex]
    Height: 44 m

    So it turned out to be a silly mistake. At least I learned from it. Thanks rl.bhat!
     
  5. Sep 18, 2009 #4
    You can also derive the formula that you need.

    Here is an alternative way to solve this problem. This will help.

    Given that the acceleration is 9.8 m/s^2 we know that

    [tex]\ddot{x}=9.8 m/s^2[/tex]

    and given that the initial velocity is 12 m/s, we can get

    [tex]\dot{x}=9.8t + 12[/tex]

    and finally, setting the initial point as 0 m

    [tex]x=\frac{9.8}{2}t^2+12t[/tex]

    Now you can plug in t=2 sec, and you get

    [tex]x=43.6 m[/tex]

    A simple calculus trick. This will help you solving more complicated problems later, without any formulae memorized. =)
     
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