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Math Help - Arclength

  1. #1
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    Arclength

    I need help on the applications of the problems below. For the total length the ball goes, I believe it is just the integral, but I cannot decide what to do next.


    A golf ball is hit with a driver and, neglecting almost all physical forces except gravity, follows
    the path
    y
    x x
    = − +
    2
    600 2
    The ball is on the ground at x = 0 and at x = 300. We will assume that the ball did not roll when
    it hit the ground. We would normally say that the drive was 300 yards long, which is the
    distance along the ground that the ball travelled. The actual distance that the ball travelled is
    given by the arclength of the parabola
    The arclength is given by the integral
    ∫ 1 [ ] ∫ 1 ( 300 )
    2
    1
    2
    2
    0
    300
    0
    300
    + y′ dx = + −x / + dx

    Problems:

    1. Use the integrator on your calculator or Simpsonís rule to evaluate this integral. How far did the ball travel?

    2. The graph of the function f axf in Figure 1 consists of three line segments for 0 ≤ x ≤ 8. Each mark along the x-axis in Figures 1, 2, and 3, and each mark along the
    y-axis in Figure 1 is 1 unit.

    a) What is the total length of the graph?

    b) What is f ′axf for 0 < x < 3 ?

    c) What is f ′axf for 3 < x < 4 ?

    d) What is f ′axf for 4 < x < 8 ?

    e) Figure 2 above shows the graph of 1 2 + f ′axf . What are the y-coordinates of the three lines that form its graph?

    f) Find the areas of the three rectangles in Figure 3.

    g) How are the answers to parts (a) and (f) related?
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  2. #2
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    skeeter's Avatar
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    sorry, but I cannot make out the syntax of your equations/expressions.

    recommend you use parentheses and regular calculator-type syntax ... or learn latex.
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  3. #3
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    Sorry, I am not really familiar with this forum. I attached a picture of the syntax, in order.
    Attached Thumbnails Attached Thumbnails Arclength-untitled.bmp  
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  4. #4
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    1. Use the integrator on your calculator or Simpson’s rule to evaluate this integral. How far did the ball travel?
    what problem are you having in calculating the arc length?

    2. The graph of the function f axf in Figure 1 consists of three line segments for 0 ≤ x ≤ 8. Each mark along the x-axis in Figures 1, 2, and 3, and each mark along the y-axis in Figure 1 is 1 unit.
    what graph in figure 1?

    what is "f axf" ??

    figures 1, 2, and 3 ???
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  5. #5
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    Sorry I suck at this.

    The arclength is just the integral, right?
    Attached Thumbnails Attached Thumbnails Arclength-untitled1.jpg  
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  6. #6
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    Quote Originally Posted by charlottepanther View Post

    Problems:

    1. Use the integrator on your calculator or Simpsonís rule to evaluate this integral. How far did the ball travel?

    use your calculator to evaluate the integral

    2. The graph of the function f axf in Figure 1 consists of three line segments for 0 ≤ x ≤ 8. Each mark along the x-axis in Figures 1, 2, and 3, and each mark along the
    y-axis in Figure 1 is 1 unit.

    a) What is the total length of the graph? find the length of each segment ... add them up

    b) What is f ′axf for 0 < x < 3 ? find the slope of the first segment

    c) What is f ′axf for 3 < x < 4 ? find the slope of the second segment

    d) What is f ′axf for 4 < x < 8 ? find the slope of the third segment

    e) Figure 2 above shows the graph of 1 2 + f ′axf . What are the y-coordinates of the three lines that form its graph?

    I'm not seeing what figure 2 means ... 1 2 + f' axf ???

    f) Find the areas of the three rectangles in Figure 3.

    g) How are the answers to parts (a) and (f) related?

    .
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  7. #7
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    Problems:

    1. Use the integrator on your calculator or Simpsonís rule to evaluate this integral. How far did the ball travel?

    312.069

    2. The graph of the function f axf in Figure 1 consists of three line segments for 0 ≤ x ≤ 8. Each mark along the x-axis in Figures 1, 2, and 3, and each mark along the
    y-axis in Figure 1 is 1 unit.

    a) What is the total length of the graph? find the length of each segment ... add them up

    b) What is f ′axf for 0 < x < 3 ? 1/4
    c) What is f ′axf for 3 < x < 4 ? -3
    d) What is f ′axf for 4 < x < 8 ? 1
    e) Figure 2 above shows the graph of 1 2 + f ′axf . What are the y-coordinates of the three lines that form its graph?

    Please refer to NEW picture

    f) Find the areas of the three rectangles in Figure 3.

    g) How are the answers to parts (a) and (f) related?
    Attached Thumbnails Attached Thumbnails Arclength-untitled2.bmp  
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