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Did I do this question right, or no?

  1. Nov 29, 2008 #1
    A bird takes 8.5s to fly from position A to position B along the path in the figure shown. Determine the bird's average acceleration.

    http://i299.photobucket.com/albums/mm286/lanvin12/physics.jpg

    Vax = (4.4m/s)sin31° = 2.26616m/s
    Vbx = Vbsin25° = (7.8m/s)sin25° = 3.2964m/s
    Vx = Vbx - Vax = 3.2964m/s - 2.26616m/s = 1.030262m/s

    Vay = Vacos31° = (4.4m/s)cos31° = 3.771536123m/s
    Vby = Vbcos25° = (7.8m/s)cos25° = 7.069200739m/s
    Vy = Vby + Vay = 3.771m/s + 7.0692m/s = 10.840736m/s

    V² = Vx² + Vy² = (10.840m/s)² + (1.030m/s)² = 118.530155m/s
    V = √118.530155m/s = 10.8895m/s

    a = v/t = 10.8895m/s) / (8.5s) = 1.2811m/s²

    tan theta = 10.84 / 1.030 = 10.522
    theta = tan^(-1) 10.522 = 84.57 degrees

    therefore...
    the bird's acceleration was 1.3m/s² [85 degrees N of E]
     
    Last edited: Nov 29, 2008
  2. jcsd
  3. Nov 29, 2008 #2
    There is no problem with the physics. However, I believe you made a mistake with angle of the components of the final velocities of the bird. It should be 35 deg insted of 25 deg.
     
  4. Nov 29, 2008 #3

    alphysicist

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    In addition to the error of using 25 degrees instead of 35 degrees that horatio89 pointed out, I think you are using the wrong trig functions. Several places it seems clear that you are using the x direction as the east and y direction as the north (which makes sense).

    The problem is, for example, in your first line, 4.4 sin(31 degrees) does not give the component in the east direction.
     
  5. Nov 29, 2008 #4
    oops! That was my mistake... the angle in the diagram should have read 25°.
    Is the answer fine otherwise?
     
  6. Nov 29, 2008 #5
    see alphysicist's post. It affects the calculation of the angle of the acceleration.
     
  7. Nov 29, 2008 #6
    I don't think I understand. What do you mean? I wrote x where I was supposed to write y, and vice versa...??
     
  8. Nov 29, 2008 #7

    alphysicist

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    I was saying that you used the sine function to find the eastward components (and the cosine function to find the north-south components) which is not correct.
     
  9. Nov 29, 2008 #8
    is this correct?

    Vx = 4.4sin31 + 7.8cos25 = 9.335
    Vy = -4.4cos31 + 7.8cos25 = -0.4745
    V^2 = 9.3^2 + (-0.47)^2
    V = 9.3m/s
     
  10. Nov 29, 2008 #9

    alphysicist

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    No; when the angles say 25 degrees N of E or 31 degrees S of E, that means both angles are measured away from the eastward direction. So the east component is the adjacent side to both angles (so you have to use cosine), and the north-south component is the opposite side from both angles (so you have to use sine).
     
  11. Nov 29, 2008 #10
    wow i'm good (sarcasm)
    maybe i'll get this right before 2009
    next attempt:

    vax/va = cos31
    vax = 3.8 m/s

    vay/va = sin31
    vay = -2.3 m/s

    vbx/vb = cos25
    vbx = 7.1 m/s

    vby/vb = sin32
    vby = 3.3 m/s

    ax = vbx - vax / t
    ax = 7.1 m/s - 3.8 m/s / 8.5s
    ax = 0.4 m/s(2)

    ay = vby - vbx / t
    ay = 3.3 m/s + 2.3 m/s / 8.5s
    ay = 0.7 m/s(2)

    a(2) = ax(2) + ay(2)
    a(2) = 0.16 + 0.49
    a = 0.8 m/s(2)

    tan(theta) = ay / ax
    tan(theta) = 0.7 m/s(2) / 0.4 m/s(2)
    tan(theta) = 1.75
    theta = 60 degrees

    Therefore the bird's acerage acceleration is 0.8 m/s 60 degrees N of E.
     
    Last edited: Nov 29, 2008
  12. Nov 29, 2008 #11

    alphysicist

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    That looks right to me. (If the percent accuracy is important, you might want to keep more digits in your calculations, but the procedure is correct.)
     
  13. Nov 30, 2008 #12
    cool, thanks for the help
     
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