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Help needed with this physics problem!

  1. Oct 1, 2012 #1
    I only have really started physics and I need help with this problem for homework.Any help is much appreciated!

    A football is kicked from the
    floor in a 7.00 m high
    sports hall with an initial speed of 20.0 m/s. What is the maximum horizontal
    distance it can
    fly without touching the ceiling until it strikes the
    floor?
     
  2. jcsd
  3. Oct 1, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Have you drawn a a picture? Let [itex]\theta[/itex] be the angle the initial velocity vector makes with the floor. Do you know how to find the horizontal and vertical components of velocity in terms of [itex]\theta[/itex]? There is no acceleration horizontally, so horizontal velocity stays is constant. Do you know how to find the horizontal distance the ball will go in t seconds?

    There is a downward acceleration, g= 9.81 meters per second per second. Do you know how to find the height of the ball after t seconds? You should have as quadratic equation for the height and that should be 0 when t= 0. Can you find the other value of t when the height is 0? (In other words, when the ball hits the ground, ending it flight.
    That will depend on [itex]\theta[/itex].) The value of x for that t is the horizontal distance the ball flies- that will also depend on [itex]\theta[/itex].

    You want to find the value of [itex]\theta[/itex] that maxizes that distance with the restriction that the height of the ball is always less than 7 meters.
     
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