The curve of a volleyball

The curve of a volleyball (without block) can by described by a very complicated function:

No fear, no calculations needed, use GeoGebra for all tasks!

1. Use GeoGebra to draw the graph of this function.

2. The position of the field in the coordinate system should be like this: x-axis for the ground, the middle line in x = 9, basic lines in both parts at x = 0 and x = 18. The height of the net is 2,43 m. What about the height of the flying ball?

3. How far from the left basic line does the ball touch the ground?

4. How far from the own basic line is the position of a volleyball player who rises his arms to a maximum height of 2,20 m?

task: M. Schwarze, Germany

Solution: The curve of a volleyball

1. What about the height of the flying ball?f’(x) = 0 => x = 5.5 f(5.5) = 3.12The highest point the flying ball reaches is 3.12m.

2. See the the Screenshot from GeoGebra (on top).

3. How far from the left basic line does the ball touch the ground?f(x) = 0 => x = 15.7The ball touches the ground 15.7m away from the left basic line.

4. How far from the own basic line is the position of a volleyball player who rises his arms to a maximum height of 2.20 m?f(x) = 2.2 => x = 11.85The distance is 11.85m.

With Geogebra the answers can be deduced from the graph as exact as possible.

But GeoGebra also can caculate with this (rather difficult) function.

Type on the input line …- f’(x) to get the derivative of f- zeros [f’,0,10] to get the zeros on this intervall - f(5,5) to get the y-value for x = 5,5- zeros[f, 0,20] to get the zeros- zeros[f-2.2, 0,20] to get the solution of f(x)=2,2

solution by Moritz H., Germany