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Vertical Projectile Motion Problem

  1. Jan 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Please check my work.

    Two students are on a balcony 19.6m above the ground. One guy throws a ball vertically downwards at 14.7m/s; at the same time the other guy throws a second ball vertically upwards at the same speed. The second ball just misses the balcony on the way down.

    2.3.1) What is the difference in the balls flight time?
    2.3.2) What is the velocity of each ball as they strike the ground?
    2.3.3) How far apart are the balls 0.8s after they are thrown?

    2. Relevant equations

    vf^2 = vi^2 + 2a*y
    delta y = vi*t + 1/2*a*t^2
    delta y = vf+vi/2 * t
    vf = vi + a*t

    3. The attempt at a solution

    2.3.1) For the ball thrown upwards I decided to first find the maximum height it reached. I used the first equation from the list and got an answer of 11.03m. I then used the third equation to find the time and got 1.5s (another 1.5s for coming down=3s). I then worked out the time for the ball thrown downwards to be 1s. My final answer for the difference in flight time is 4-1=3s.

    2.3.2) Each ball would strike the ground at the same speed.
    vf = vi+a*t
    = 14.7+9.8*1
    = 144.06m/s

    2.3.3) Using the heights of the two, I worked the distance for the first ball to be 8.624m and the second ball to be 14.896m. Subtracting the two would give a distance of 6.272m as my final answer.

    All I am asking is for someone to please check my work because I am not sure if I have approached this problem in the correct way.
     
  2. jcsd
  3. Jan 28, 2013 #2

    rude man

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    Check the number in red above! Otherwise all is good.
     
  4. Jan 28, 2013 #3
    I think the first ball should be 14.896 and the second ball 8.624. Is that my mistake?
     
  5. Jan 28, 2013 #4

    rude man

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    Check the items in red above!
     
  6. Jan 28, 2013 #5
    Ok im a bit confused, but this is how I got 14.896m:
    delta y = 14.7*0.8 + 1/2(9.8)*0.8^2
    = 14.896m

    Is there something I did wrong?
     
  7. Jan 28, 2013 #6

    rude man

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    Should that number be + or -?
     
  8. Jan 29, 2013 #7
    If the answer should be negative, Why?
     
  9. Jan 29, 2013 #8

    rude man

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    Because when you came up with y1 = +8.624m you defined y = 0 to be the balcony height, so anything below the balcony is negative. It should also be obvious that the second ball will be lower in height than the first, not higher as you had it.

    So y1 = vi*t - gt^2/2 = 8.624m (ball tossed up but g is down)
    y2 = -vi*t - gt^2/2 = -14.896m (ball tossed down & g is down)
    y1 - y2 = 2vi*t = you fill this one in!

    Just keep track of signs & you'll be fine.
     
  10. Jan 29, 2013 #9
    So the final answer is 23.52m apart?
     
  11. Jan 29, 2013 #10

    rude man

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    Yep.
     
  12. Jan 29, 2013 #11
    Ok, thanks for your help
     
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