Projectile Motion Horizontal Displacement Equation

[ArbazAlam]

Homework Statement

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(v_i)²sin2[theta])/19.6

Could somebody please confirm this?

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?

 

[tiny-tim]

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(v_i)²sin2[theta])/19.6

Could somebody please confirm this?

Hi ArbazAlam!

(have a theta: θ)

Yes, that's right.

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

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?

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

 

[ArbazAlam]

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