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Free Fall Tennis Ball Question

  1. Aug 14, 2013 #1
    1. The problem statement, all variables and given/known data

    A tennis ball is thrown upward with and reaches height of 18 m. What maximum height can reach this ball on the where acceleration of free fall is 6 times less than g? In both cases initial velocity is same. [sic] (excuse my physics teacher's grammar, don't shoot the messenger! :tongue:)

    g= 9.81 m/s2
    x= distance or displacement
    v= velocity
    a=acceleration (which is g)

    Max Height is at V=0

    2. Relevant equations

    [itex]V=\sqrt{2gx}[/itex]
    [itex]ΔX=V_it + (1/2) at^2[/itex]

    3. The attempt at a solution

    [itex]9.81/6=1.64[/itex]

    [itex]V^2=2(1.64)x[/itex]

    Initial velocity in a free fall is 0 m/s, right? If so, v=0 and then x=0

    In such a case, it would be odd for the max height to be 0 m.
     
    Last edited: Aug 14, 2013
  2. jcsd
  3. Aug 14, 2013 #2
    If the ball is thrown upward, then its initial velocity cannot be zero.

    Note the formulation does not require that the initial velocity be zero; it just says it is the same in both cases.
     
  4. Aug 14, 2013 #3
    So, I can just use any velocity?

    Or must I use a velocity that intersects?

    Considering time is neither given nor required, can I use

    [itex]V_f = V_i+at[/itex]?

    [itex]V_f=0[/itex] to find the maximum.

    I use the gravities as the slope. However, the lines intersect at the origin, where time and velocity equal 0.

    [itex]0 = -1.64 t[/itex]

    [itex]0 = -9.81 t[/itex]
     
    Last edited: Aug 14, 2013
  5. Aug 14, 2013 #4

    gneill

    User Avatar

    Staff: Mentor

    You can find the initial velocity using your first Relevant Equation for the stated conditions that the ball reaches a height of 18 m when gravity is g.

    Note that you are taking advantage of the fact that ideal free-fall trajectories are symmetric with respect to time reversal, so if a ball launched upwards with some velocity V reaches maximum height H, then a ball dropped from height H will reach a final velocity V just before impact with the ground.
     
  6. Aug 15, 2013 #5
    Does that really matter what the initial velocity is numerically? You know it is the same. That means the initial kinetic energy is the same.
     
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