Math Help - Firefighter problem

1. Firefighter problem

1. The problem statement, all variables and given/known data

A firefighter on the street is trying to spray water from a hose to a building a horizontal distance x1 through a window a height h above the height of the hose (see figure in image below). For a given initial speed vo of water from the hose, we would like to future out if the water will reach the window, and if it does, then what angle (and how many angles are there) does he need to aim the hose at. (The questions are in the image below)

2. Relevant equations

t = d / (v cos θ)
h = -4.9 sin θ t^2 + v sin θ t

I posted this on a different web forum, however, I had no luck with hints. I figured it may be because it is very math intense, that is why I am posting this on here. My question, is how can you solve for b) (i-iii) if you have so many unknown variables?

2. Re: Firefighter problem

when solving for $tan \theta_0$, you can assume all other variables are constant.

the equation is a quadratic in $tan \theta_0$, have you been taught how to tell if a quadratic has 0,1 or 2 solutions? if so try and use that method

3. Re: Firefighter problem

Originally Posted by SpringFan25
when solving for $tan \theta_0$, you can assume all other variables are constant.

the equation is a quadratic in $tan \theta_0$, have you been taught how to tell if a quadratic has 0,1 or 2 solutions? if so try and use that method
How can you just assume that all other variables are constant when there are so many unknowns?

4. Re: Firefighter problem

Originally Posted by Barthayn
How can you just assume that all other variables are constant when there are so many unknowns?
They're explained:

• g = acceleration due to gravity
• v_0 = the initial speed of the water (assume it's force is too low to alter the angle)
• x = the horizontal distance (it is heavily implied the firefighter stands still)
• h = the height of the fire (constant)

5. Re: Firefighter problem

I understand that, however, I don't understand how one can calculate the angle if we do not what the numerical variables are representing.

6. Re: Firefighter problem

"solve for $\tan \theta$" does not necessarily mean "tell me what number $\tan \theta$ is".

it means: find the value of $\tan \theta$ in terms of the other variables.

Only when you get to part (c) do you have to get a numerical answer.

7. Re: Firefighter problem

Thanks. I asked a math teacher what it meant today and she said the same thing as I initially thought but I thought it was wrong. Thank you for all your help too.