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1d motion questions

  1. Sep 10, 2012 #1
    1. The problem statement, all variables and given/known data
    a rock is thrown nearly vertical upward from the edge of a tall building of height H. it just misses the edge of the building on the way down and strikes the ground T seconds after being thrown. given H, T

    determine the initial velocity of the rock
    the max height it reaches above its starting point
    the time to reach its max height


    2. Relevant equations

    v= v_0 + at

    x = x_0 + v_0*t + 1/2*a*t^2

    v^2 = v_0^2 + 2a(x - x_0)




    3. The attempt at a solution

    x_0 = H
    x = 0
    v_0 = ?
    v = ?
    a = g
    t = T

    with these as inputs I don't see how I can manipulate algebra to get the things I want. this is a recurring theme with the rest of my homework it seems:




    a flowerpot falls off a windowsill and falls past a window below. a person inside the building notices that it takes T seconds to go from the top to the bottom of the window. the window is h meters high. given h, T

    determine how far above the window is the windowsill.

    v= v_0 + at

    x = x_0 + v_0*t + 1/2*a*t^2

    v^2 = v_0^2 + 2a(x - x_0)


    x_0 = 0
    x = q + h (figuring out q is the goal)
    v_0 = 0
    v = v
    a = g
    t = T


    one again i feel like when i mess with the algebra i end up going in circles where I can't get everything solved within means of the terms given... hurts my head. i think im doing something fundamentally wrong, let me know.
     
  2. jcsd
  3. Sep 10, 2012 #2
    1. x_0 = H
    x = 0
    v_0 = ?
    v = ?
    a = g
    t = T
    ......
    x=H
    x_0=0

    2. x=u2/2a

    h=ut+0.5at2
     
  4. Sep 10, 2012 #3
    With [itex]v_0[/itex], the object can reach the maximum height [itex]h[/itex] (relative to the top of the building). That gives you an equation relating [itex]v_0[/itex] and [itex]h[/itex]. It takes [itex]T_u[/itex] to lose the initial speed [itex]v_0[/itex] going upward to the maximum height. That gives you an equation relating [itex]v_0[/itex] and [itex]T_u[/itex]. It takes [itex]T_d[/itex] to fall from [itex]H + h[/itex] to the ground. That gives you an equation relating [itex]H[/itex], [itex]T_d[/itex] and [itex]h[/itex]. And [itex]T_u + T_d = T[/itex]. So you have four equations and four unknowns [itex]v_0[/itex], [itex]h[/itex], [itex]T_u[/itex] and [itex]T_d[/itex], which you can solve.
     
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