# Vectors in Volleyball (finding distance ball will go)

1. Mar 3, 2013

### cd79443

1. The problem statement, all variables and given/known data
A sand volleyball player attempts a jump serve. The player is 9.0 meters away from the net, which is 2.43 meters high. If the volleyball player hits the ball at the top of his jump (where the ball is 3.25 meters above the ground) and hits it an angle of 2 degrees below the horizontal, determine the following:
1) What is the minimum velocity he can hit the ball with and still have it go over the net?
2)If the opposite end of the court is 9 meters behind the net (18 meters from where the server is) will the volleyball land inbounds?

2. Relevant equations
Pythagorean theorem
$x = x_0 + V_y t - 0.5g t^2$
$x = x_0 + v_0x t + 0.5g t^2$

3. The attempt at a solution
part 1) I think I was able to work out part 1 eventually, I came up with 28m/s but I'm not positive I solved it correctly. It's mostly part 2 that's giving me trouble!

part 2) I've drawn pictures of the triangles which is difficult to illustrate on here. But using the triangles from part one I know that the found vector (hypoteneuse on my triangle) is 28 m/s at 2 degrees below the positive horizontal. From that I found that the x component is 27.9829 m/s and the y component is 0.977 m/s. So all that is found from part 1 (which I'm still not positive about) but I'm not sure how to apply it to part two. I'm not even sure of what variable I'm trying to find! I know that the x component of the vector should be the same as in part 1 (27.9829 m/s) but the y component should be different, which will mean the angle will be different as well. But I'm just not sure where to go from here. Some help would be really appreciated!

2. Mar 3, 2013

### haruspex

That's what I get.
There are several ways. E.g. using the velocity calculated, find out when it would hit the ground, then see how far it would have travelled horizontally in that time.
Or, having gone to the trouble of finding a formula for the velocity in the first part you could just change the height and distance inputs (from 3.25-2.43 and 9 to 3.25 and 18, respectively) to find out the velocity that it would make it land on the baseline. Compare that with the velocity required to clear the net.

3. Mar 3, 2013

### cd79443

Great, I think I got it now. Thank you so much!

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