Maximum height water can be projected onto a wall

[tycoon515]

Homework Statement

H3-1 Determine the maximum height on the wall to which the firefighter can project water from the hose if the speed of the water at the nozzle is 20 m/s.
The firefighter stands 18 m away from the wall and holds the nozzle 1.2 m above the ground.

Homework Equations

The Attempt at a Solution

This is my work. What I did was solve for the time it took for the water to travel 18 m forward as a function of theta. Then I plugged this time into the uniform acceleration kinematic for vertical position to get height at the wall as a function of launch angle. I then maximized height using calculus and got an answer. My professor claims that my approach is not valid for this problem and suggests that the process shown in the attached solution sheet hw3s.pdf is the way to go. On the solution they start by saying that height is maximized when dy/dt = 0, so they assert that dy/dt at the wall must be zero. I'm skeptical of their approach. Here's my work:

 

[BvU]

Hi Ty,

Can read the exercise and the book solution. Agree. Hard to read your writing, could you type it out ?

 

[TSny]

tycoon515, I agree with your answer. The max height on the wall does not correspond to the max height of the trajectory.

 

[BvU]

TSny read better than I. Once I turned your page over 90 degrees it became legible. Book answer is way wrong.
Hats off for your work !