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Why is the sign in the formula Δy=VoyT - (1/2)at² negative in this problem

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data
    A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0º to the horizontal.
    (a) By how much does the ball clear or fall short of clearing the crossbar?
    (b) Does the ball approach the crossbar while still rising or while falling?

    2. Relevant equations
    1.)Vox= Vo*CosΘ
    2.)Voy= Vo*SinΘ
    3.)Δx=x=VoxT where T (caps) is equal to time and not period.(its caps to discern from the sub 'ox')
    4.)Δy= VoyT - (1/2)gt²

    3. The attempt at a solution

    Vxi = 20Cos(53)= 12.07 m/s
    Vyi = 20Sin(53)= 15.97 m/s

    36.0 m = (12.03 m/s)t → t = 3.00 seconds

    Δy= (15.97 m/s)(3.00 seconds) - (1/2)(9.8 m/s²)(9.00 seconds²)
    Δy = 3.9 meters
    Clears by .9 meters...approximately
    (the answer is .889 m while descending)

    So, I obviously figured out how to do the problem, but I want to know why Relevant Equation 4.) requires me to use a negative sign instead of a positive one.

    May someone shed some light. Im obviously missing something very similiar. I tend to complicate things too much.
    Last edited: Nov 22, 2008
  2. jcsd
  3. Nov 22, 2008 #2


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    Homework Helper

    The direction of velocity and acceleration matters.

    You choose Vy as positive y, then g is going to be negative.

    It starts out with Vy and all the time gravity is working to reverse it and return it to earth.

    Vy gets smaller until it is 0 at max height, then it becomes negative on its downward plunge.
  4. Nov 22, 2008 #3

    I can not thank you enough! Thank you very much!
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