# Homework Help: Projectile Motion Horizontal Displacement Equation

1. Sep 18, 2008

### ArbazAlam

The problem statement, all variables and given/known data

A fire hose held near the ground shoots water at a speed of 7.5 m/s. At what angle(s) should the nozzle point in order that the water would land 3.0 m away?

The attempt at a solution

I remember from engineering there was a single equation you could use to find the horizontal displacement of an object given its initial velocity and projected velocity. I tried deriving it and came up with this:

x = (2(vi)2sin2[theta])/19.6

It also asks: Why are there two different angles? I know how to describe this logically, but my teacher usually prefers a more mathematical answer. Would I just say that there are two values for theta that yield the same sine value?

2. Sep 18, 2008

### tiny-tim

Hi ArbazAlam!

(have a theta: θ)

Yes, that's right.

(though why didn't you just say x = (vi)2sin2θ/9.8 ? )

Yup … that would do … you could even say how the two values are related!

3. Sep 18, 2008

### ArbazAlam

Thank you! I didn't even notice those units canceled out. And thank you for the theta.