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Homework Help: Projectile Motion Kinematics Problem

  1. Mar 7, 2010 #1
    1. The problem statement, all variables and given/known data

    Will a ball, kicked at 14.0 m/s vertically and 9.0 m/s horizontally, clear a bar 3.0 m high and 20 m away from the kicker? Solve.

    2. Relevant equations

    Kinematics Equations.

    3. The attempt at a solution

    Haven't encountered this type of problem, didn't know where to start.
  2. jcsd
  3. Mar 7, 2010 #2


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    Homework Helper

    Horizontal motion , and vertical motion, are independent ... linked by TIME .

    re-word the question to make TIME explicit :
    "will the ball be at least 3m high WHEN it gets to the bar at x=20m ?

    After you figure out what time that happens, you can find its height.
  4. Mar 8, 2010 #3
    ok, so im trying to learn these ones too. here is what i know. 14m/s vertical vector component of velocity. how high will the ball travel? well, this a kinematic equation problem.
    Vo = initial velocity = 14m/s. (says in the question)
    V = final velocity (when the ball is at the top of its flight path, this is) = 0
    a = acceleration = -9.8m/s^-2 (only force acting on this object)
    t = time = ?
    x = change in x, or change in displacement, or change in distance vertically = ?

    but with three knowns, we can find a fourth. in this case it would be good to see how high the ball is going to go, so we want to find 'change in x'

    we know that
    V^2 = Vo^2 + 2*a*x
    this is on of the five kinematic equations derived from the ideas that velocity = change in distance/ change in time, and, acceleration = change in velocity/ change in time

    so, rearanging mathematically this formula, to isolate x, we get
    ((V^2) - (Vo^2)) /2*a = x
    now we can substitiute in the values we know to solve for x
    ((0-14^2))/2*-9.8 = x
    10 = x is what i get. so this tells us the ball will get to a maximum height of 10m at some point. this is the first thing we need to know
  5. Mar 8, 2010 #4
    so then, to find the time it takes for the ball to get to the maximum height
    use the formula (V-Vo)/a = t
    this gives a time of 1.43s

    to find how far horizontally this point is from where the ball is kicked, now look at the horizontal component. 9m/s. the ball is travelling with a velocity of 9m for 1.43 s,
    using the formula v = change in distance/change in time, rearange this to get
    velocity*time = change in distance
    9*1.43= 12.87m. so it has not yet reached the bar 20m away.
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