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Freefall body problem

  1. Aug 19, 2015 #1
    1. The problem statement, all variables and given/known data
    You throw a ball vertically upward from the roof of a tall building. The ball leaves your hand at a point even with the roof railing with an upward speed of 15.0 m/s; the ball is then in free fall. On its way back down, it just misses the railing.
    Find (a) the position and velocity of the ball 1.0 s and 4.0 s after leaving your hand;
    (b) the velocity when the ball is 5.0 m above the railing;
    (b.1) How long will the ball reach 5 m
    (c) the maximum height reached and the time at which it is reached; and
    (d) the acceleration of the ball when it is at its maximum height.

    2. Relevant equations
    Freefall equation like Vf=Vo-gt and etc

    3. The attempt at a solution
    T at 1
    a.) ΔY = (15 m/s)(1 s) - (1/2)(9.8 m/s^2)(1 s)^2
    ΔY = 10.1 m

    T at 4
    ΔY = -18.4 m

    V at 1
    Vf = (15 m/s) - (9.8 m/s^2)(1)
    = 5.2 m/s

    V at 4
    Vf = -24.2 m/s

    b.) Vf^2 = Vi^2 - 2gΔy
    Vf^2 = (15 m/s)^2 - (2)(9.8 m/s^2)(5 m)
    Vf^2 = 11.27 m/s

    b.1) (11.27 m/s) = (15 m/s) - (9.8^2)(t)
    t = 0.38

    5 m = (15 m/s)(t) - (1/2)(9.8 m/s^2)(t)
    t = 2.68

    I'm a bit confuse here I got 2 different answer in this part. Really need a big help here

    c.) a = Δv/Δt -> t = Δv/a -> t = (15 m/s)/(9.8 m/s^2)
    tmax = 1.5306

    Δymax = (15 m/s)(1.5306 s) - (1/2)(9.8 m/s^2)(1.5306 s)^2
    y = 11.48

    d.) The answer is -9.8 m/s^2 right? Constant?
     
  2. jcsd
  3. Aug 19, 2015 #2
    For question b.1) you wrote 5=15t-9,8*0.5t while it should be 5=15t-9.8*0.5T^2
     
  4. Aug 19, 2015 #3
    lol im such a stupid one

    is my c.) and d.) right?
     
  5. Aug 19, 2015 #4

    haruspex

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    Yes, c and d are right.
     
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