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2-D motion: projectile motion of football

  1. Sep 26, 2008 #1
    Hi, I have been having a lot of trouble with this problem. I have been trying to figure it out for hours with limited success... Any help would be very much appreciated!

    1. The problem statement, all variables and given/known data
    A football is thrown toward a receiver with an initial speed of 16.9m/s at an angle of 38.6 degrees above the horizontal. At that instant, the receiver is 17.4m from the quarterback. The acceleration of gravity is 8.81m/s2. With what constant speed should the receiver run to catch the football at the level at which it was thrown? Answer in units of m/s.


    2. Relevant equations

    V0cosθ= Vy
    V0sinθ= Vx
    1. Range= (V0^2 sin2 θ)
    ------------
    g
    2. displacement X= Vxt
    3. delta X= V0t + 1/2 at^2


    3. The attempt at a solution

    I drew a picture, and because the problem says it is caught on the same level, I assumed I could use the range formula. So I did that and found the total Range (delta X). Then, I plugged that into the 2nd equation to find the total time the football is in the air.
    I took the answer I got from the Range formula (delta X) and subtracted 17.4m from it because that is how far the receiver will have to run. Then, I used the 2nd equation again to find how long it took the football to travel 17.4 meters. I took that time and subtracted it from the total time to find out how much time the receiver would have to run and catch the football. Then, I used the Delta X/ that time to get the Vx. Are my steps right? Because when I tried to submit the answer online, it said my answer was incorrect...
    When I did all these steps, I got an answer of 13.20769597 m/s.
     
  2. jcsd
  3. Sep 26, 2008 #2
    Wow, this receiver should try out for the NFL. =)

    You are right in applying the range formula. You want to know the "total time" that the ball is in the air (this is your mistake). This is how much time the receiver has to move to catch the ball.
     
  4. Sep 26, 2008 #3
    oh i see my mistake. Thanks a lot!
     
  5. Sep 26, 2008 #4
    this is ticky as far as component problems go...
    I know nothin about a range formula, I'll assume its a variation of the basics...

    1) okay first you break down the ball's velocity into components.

    that means Vx = Vcos(38.6) and Vy = Vsin(38.6)

    2) next we wanna know how long this ball is in the air. The time the ball takes going up is equal to the time it take for the ball to come down! So find the time it takes to go up and double it... (and A = -9.81 m/s^2)

    V final = V initial + A(t)

    2t = total air time.

    3) Find the distance the ball will travel horrizonally.

    X = V (x component) times t

    4) Find out how far away the ball will land from the reciever

    ball distance - where the reciever starts = distance receiver must cover

    5) at step 2 you found how long the ball will be in the air. the reciever must cover the distance in part 4, in the time the ball takes to reach that spot from step 2. so

    V = X/T, V reciever = step 4 distance/step 2 time

    take the time to picture whats going on in each step.
     
  6. Sep 26, 2008 #5
    thanks, thats a very detailed explanation :)
     
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