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What direction must the fielder take

  1. Oct 14, 2014 #1
    At t=0 a batter hits a baseball with an initial speed of 28m/s at a 55 ∘ angle to the horizontal. An outfielder is 85 m from the batter at t=0 and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of 22 ∘ with the plane in which the ball moves (as shown in the figure).

    GIANCOLI.ch03.p098.jpg

    What direction must the fielder take to catch the ball at the same height from which it was struck? Give the angle with respect to the outfielder's line of sight to home plate.
    Express your answer to two significant figures and include the appropriate units.

    Attempt

    First of all, I couldn't understand what angle it is talking about. But I've managed to do some computations related to the baseball.

    Time for the same height = (28*sin(55))*2/g = 4.68 s
    Range = 28*cos(55)*28*sin(55)*2/g = 75.16 m

    When you draw a triangle with 75, 85 and the distance that will be run, you need an angle to find the unknown length. Is it 22 degrees in this case?

    Assuming that degree 22, by cosine theorem you get the distance outfielder runs = 32m.

    But as I still don't have an idea what angle is to be found, I can't go any further than this.
     
    Last edited: Oct 14, 2014
  2. jcsd
  3. Oct 14, 2014 #2
    Funny, I have done the solution right now.
    With the triangle I've formed, say the angle between 85 and 75 is alpha.

    By the sine theorem:
    sin(22)/32 = sin(alpha)/75
    you have the correct answer from this equation, 61.

    Can somebody just show what angle I just found out? Because I am beginning to feel like this.
    Even-I-Dont-Knowwhat-i-am-doing.jpg
     
  4. Oct 14, 2014 #3

    mfb

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    2016 Award

    Staff: Mentor

    You found the angle between the green arrow and the line marked with 85.
     
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