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Math Help - tennis

  1. #1
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    tennis

    I have this problem in my book and I keep coming up with the wrong answer.

    "A ball is served from the center of the basemline into the deuce court. If the ball is hit 9 ft above the ground and travels in a straight line down the middle of the court, and the net is 3 ft high, how far from the base of the net will the ball land if it just clears the top of the net?"

    Additional information: The court is 27 ft x 78 ft. The duece court is 21 ft long and the remainder of the court is 18 ft.

    I keep getting that the ball would land 13 feet from the bottom of the net, however the answer in the back of the book says it is 19.5 ft. Any guidance would be appreciated.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, jlefholtz!

    I think your diagram is off . . .


    A ball is served from the center of the basemline into the deuce court.
    If the ball is hit 9 ft above the ground and travels in a straight line down the middle of the court,
    and the net is 3 ft high, how far from the base of the net will the ball land if it just clears the top of the net?

    Additional information: The court is 78 feet long.
    Code:
          *
          |     *
          |           *
          |                 *
         9|                 |     *
          |                3|           *
          |                 |                 *
          *-----------------*-----------------------*
          : - - - 39  - - - : - - - - - x - - - - - :

    From similar triangles, we have: . \frac{x}{3} \:=\:\frac{x+39}{9}

    Solve for x\!:\;\;9x \:=\:3(x+30) \quad\Rightarrow\quad 9x \:=\: 3x + 117 \quad\Rightarrow\quad 6x \:=\:117

    Therefore: . x \:=\:\frac{117}{6} \;=\;19.5\text{ feet}

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