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Homework Help: Need work checked(dyanmics projectile problem)

  1. Mar 25, 2010 #1
    First time poster, site looks very informative so I thought I would make a post. This is for Mechanics class and now covering Dynamics. This is my take home problem.

    A basket ball player shoots when she is 5 m from the backboard. Knowing that the ball has an intial velocity Vo at an angle of 30⁰ with the horizontal, determine the value of Vo when d is equal to (a) 228 mm, (b) 420 mm.


    1. The problem statement, all variables and given/known data
    given info:
    x: player is 5M from back board
    y: initial height of ball 2m from floor, hoop is 3.048m from floor
    angle: 30⁰
    d: this is the distance from the back board or offset

    2. Relevant equations
    x = Vo cos(30)*t
    y = Yo + Vo*sin(30)t - 1/2gt^2

    3. The attempt at a solution
    x = 5m - .288m = 4.772m
    4.772m = Vo*cos(30)*t
    Vo = 4.772/cos(30)

    y = 2m + (4.772m/cos(30))*sin(30)t - 1/2(9.81)t^2
    t = .987s

    Vo = 4.772/cos(30)*(.987s)
    = 5.44m/s

    Using same method
    b = 5.13m/s
    Found a picture for the problem on the net for better clarity:
    http://books.google.com/books?id=A_...esnum=3&ved=0CBEQ6AEwAg#v=onepage&q=&f=false"
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Mar 29, 2010 #2
    So its been several days now and no response. Perhaps I would have had better luck under the Physics section? If I did not explain the problem clearly I posted a link to the problem which includes a picture. I am pretty confident my work is correct but would feel a lot better if someone else can confirm this work accurate.
     
  4. Mar 29, 2010 #3

    PhanthomJay

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    Equations look good, but check your math and you have a typo , should be Vo = 4.772/cos(30)*t (you left out the 't'). What value are you using for y?
     
  5. Mar 29, 2010 #4
    I am solving for 't', so y = 0. But I use 2m for my Y0.
    Here is a little more detail in my steps:
    x = Vo cos(30)*t
    4.772m = Vo*cos(30)*t
    Vo = 4.772/cos(30)t
    y = Yo + Vo*sin(30)t - 1/2gt^2
    0 = 2m + (4.772m/cos(30))*sin(30)t - 1/2(9.81)t^2
    (4.9)t^2 = (4.775)t^1/2
    t = .987s
    Vo = 4.772/cos(30)*(.987s)
    = 5.44m/s
     
  6. Mar 29, 2010 #5
    I am not sure about my value for 't'. I take the square root of both sides and solve for t, I get .987 when 4.9 over 4.775 or 1.013 when 4.775 over 4.9.
     
  7. Mar 29, 2010 #6

    PhanthomJay

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    y is not 0 when the ball hits the basket.
    you keep making the same error by omitting the t I've added in red.
     
  8. Mar 29, 2010 #7
    Geeze I cant believe I mist that. Okay so:
    Yo = 2m
    Yf = 3.048m
    3.048m = 2m + (4.772m/cos(30)t)*sin(30)t - 1/2(9.81)t^2
    t = 1.7s
    Vo = 4.772/cos(30)*(1.7s)
    V0 = 9.37m/s
     
  9. Mar 29, 2010 #8

    PhanthomJay

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    you seem to be having trouble with your math

    1.048 = (4.772/cos30)sin30 -1/2(9.81)t^2

    solve for t = ???
     
  10. Mar 29, 2010 #9
    Ok, this is what I am doing:
    4.9t^2= -1.048+(4.772/cos30)sin30 t's cancel on right side?
    taking square toot to both sides and solving for t:
    2.21t= 1.306
    t=.59s

    I am moving t^2 to the left side, I dont know why I am now getting different valudes for t.
     
  11. Mar 29, 2010 #10

    PhanthomJay

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    Yes, that looks better. I'm not sure what you were doing before.
     
  12. Mar 29, 2010 #11
    Thank you Phantom, I wasnt taking care of my 't' because I had it written incorrectly on a different set of notes. If I had took the time to think about it, I probably would have corrected it.
     
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