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Homework Help: Initial velocity and time of motion through water

  1. Feb 25, 2016 #1
    1. The problem statement, all variables and given/known data
    What initial velocity has to have a ball at the height [itex]h=1m[/itex] in order to sink in the water to depth of [itex]s=4m[/itex]? How long is the motion of a ball through water? A ball is made of material that has density [itex]\rho=770 kg/m^3[/itex]. Surface tension and friction are negligible.
    2. Relevant equations
    Classical mechanics - free fall
    3. The attempt at a solution
    Ball will fall on water surface after [itex]t_1=\sqrt{\frac{2h}{g}}[/itex].
    Time of falling to the bottom of water is [itex]t_2=\sqrt{\frac{2s}{g}}[/itex].
    Motion through the water is [itex]t_2-t_1=0,451 s[/itex].
    Is this correct?
    How to find the initial velocity? Why is the density of a ball [itex]\rho[/itex] given?
  2. jcsd
  3. Feb 25, 2016 #2
    Yes, you are correct in that you use classical mechanics. However, you must also think about other forces that could be present, not just gravity.
    What forces are exerted on an object partially or totally immersed in a fluid? How would density be relevant?
  4. Feb 25, 2016 #3
    I would say, no, the time formulas quoted are for object's Free-Falling from rest. The problem states that the ball has an initial {unknown} velocity when dropped in air from a height = 1 m. Then it will also have the necessary initial velocity when it enters the water to drive it down a distance = s = 4 m. Both in air and in water formulas are of the form: d = Vo(t) + 1/2gt²
    Last edited: Feb 25, 2016
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