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Homework problem on projectile motion

  1. Jun 20, 2011 #1
    1. The problem statement, all variables and given/known data
    Question: James and Steve have a contest to see who can kick a football further. James kicks the football at an angle up of 57 degrees, and a speed of 75m/s. Steve kicks the ball with a speed of 100m/s, at an angle up of 48 degrees? Who wins the contest?

    Vix=75cos57
    viy=75sin57


    2. Relevant equations
    First, I don't really understand what variables I have and don't have. I know you can find Vix but doing 75cos57 and viy by doing 75sin57. I think I have to find time but like I said I am don't understand what variables I have or what variables I need.

    Secondly, is this a two part questions? The fact that there are two different people is really confusing me.


    3. The attempt at a solution
    okay here is my small attempt. I assumed that vfy=0 and vfx=0 (this doesn't seem right but I tried it anyway). Then I pulled what variables I think I had into this equation: vfx=vix+axt
    With the number it looked like this 0=40.8-9.81(t)
    -40.8=-9.81
    t=4.15

    After this I just didn't know what to do.

    What I need help with: I need help clarifying the variables and knowing what variables I need
    Knowing what equation to use
     
  2. jcsd
  3. Jun 20, 2011 #2

    gneill

    User Avatar

    Staff: Mentor

    Hi Kalix, welcome to PF.

    The problem is asking you to determine who's ball will travel furthest. So in that respect you have two separate (yet similar) problems to solve; they just have different numbers to plug in.

    Each case involves a ball being kicked from ground level with some initial speed and at some initial angle, and you want to find how far the ball will travel before it hits the ground once again. In order to address this problem you first have to realize that the ball's trajectory is governed by two components: the horizontal motion, which has a constant velocity, and the vertical motion which is affected by gravitational acceleration. It's this latter motion that determines how long the ball stays in the air, while the former determines how far (horizontally) the ball will travel while it remains airborne. So, you need to write the equations that govern both of these motions and solve for the time of flight and then the horizontal distance covered in that time.

    Your known values are initial speed, launch angle, and the acceleration due to gravity (in the vertical direction). Your unknowns (variables) include time, y position, and x position.

    Does that help?
     
  4. Jun 20, 2011 #3
    It helps some but I am still confused about what to do with the 2 different angles. Does this mean that I will have 2 different vix and viy values? Also do the vfy and vfx values equal 0. I assumed that in my first attempt of the problem but I wasn't sure if I was correct or not.
     
  5. Jun 20, 2011 #4
    treat it as two seperate questions and solve for the total distance kicked and whichever has the longest distance kicked, obviously wins. Furthermore, treat the x and y components seperately, so to start you off, take the y component and solve for the time because vertical motion is independent of the horizontal. Once you have your time you should be on your way.
     
  6. Jun 20, 2011 #5
    Okay I think i am starting to understand. Just one more clarifying question: Is the distance kicked equal to x?
     
  7. Jun 20, 2011 #6
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