SOLUTION: A narrow arch supporting a stone bridge is in the shape of half an ellipse and is 36 m long and 14 m high. A person standing at one focus plays with a ball by throwing it against t

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Question 1182930: A narrow arch supporting a stone bridge is in the shape of half an ellipse and is 36 m long and 14 m high. A person standing at one focus plays with a ball by throwing it against the arch. The ball always bounces off the arch once and strikes the same point on the ground (the other focus).
a. How far apart are the person throwing a ball and a point on the ground at which the ball strikes?
b. What is the height of the arch exactly below the position of the person?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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A narrow arch supporting a stone bridge is in the shape of half an ellipse and is 36 m long and 14 m high.
A person standing at one focus plays with a ball by throwing it against the arch.
The ball always bounces off the arch once and strikes the same point on the ground (the other focus).
a. How far apart are the person throwing a ball and a point on the ground at which the ball strikes?
b. What is the height of the arch exactly below the position of the person?
~~~~~~~~~~~~~ 

The semi-axes are  a = 36/2 = 18 meters (the major semi-axis) and b = 14 meters (the minor semi-axis).


Hence, the distance from the focus to the center of the ellipse is


    c =  =  = 11.314 m.


The distance between the focuses is twice this value, i.e.  2*11.314 = 22.628 meters.    ANSWER


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For info about the elements of an ellipse, see the lesson
    - Ellipse definition, canonical equation, characteristic points and elements
in this site.



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