To reach each zone (for explanation of a zone see "the game" page), an initial velocity is

required. Our job was to calculate the different initial velocities necessary to

project the ball into zone 3 vs. zone 6. The height of the server and the passer was

estimated to be 1.85 meters.

     The assumptions made during the analysis were a flight angle of 60 degrees

above the horizontal. We also assumed no air resistance nor energy lost due to

rotation on the ball. The height of the women’s volleyball net is 2.55 meters and

the ball is passed from the same height from which it is served. The two zones

analyzed in our study were located 13 meters (for zone 3) and 19 (for zone 6)

respectively from point of serve. Because the initial height of the ball is equivalent

to the final height of the ball we were able to use the range equation to find the

initial velocity of the balls. The range equation is as follows: R=Vo²*sin2θ/g, θ,

being the angel, and g being the acceleration due to gravity  or 9.8 m/s2.

For zone 3 the overall range was 13 meters and the initial velocity necessary for the

ball to move the required distance was 12. 1 m/s. It must be noted that while the

ball is in flight the force of gravity also acts upon it and this force creates the

parabolic shape of the flight of the ball. To be sure that the ball would clear the

height of the net, the height equation was used to determine the height of the ball

at a distance of 10 meters from the server. This is equation is the following: y=Vyt –

1/2gt² with t representing the time, g the acceleration due to gravity. Vy

represents the y-component of the velocity (obtained using trigonometry). This

produced a height of 4.0 meters, which would easily clear the height of the net.

    We also calculated the maximum height of the ball’s flight to be sure the height

value calculated at the 10 meter mark was between the net height and the

maximum value of flight. We used the height equation to determine that maximum

height. The height equation is h=Vi²Sin2θ/2g. For zone 3 the maximum height at

60-degree angle was 4.22 meters.

Zone 6

The same calculations were made for zone 6, which was 19 meters away from the

serving point. The overall velocity was 14.7 m/s. This velocity makes sense to be

greater than the velocity necessary to reach zone three because zone 6 is six meters

farther from the point of serve than zone 3. Again we checked to make sure the ball

would clear the net. The height at 10 meters from the serving point was 5.3 meters.

The maximum height of the ball was 6.2 meters.

Ogonna Nnamani of Stanford University