A fire hose ejects a stream of water at an angle of 33.4 ° above the horizontal. The water leaves the nozzle with a speed of 20.1 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

To find the horizontal distance at which the water should hit the highest possible fire, we need to analyze the projectile motion of the water stream.

Projectile motion can be broken down into two independent components: horizontal and vertical. In this case, the vertical component is affected by gravity, while the horizontal component remains unaffected.

Let's break down the given information:
- Angle of projection (θ) = 33.4°
- Initial speed (vi) = 20.1 m/s

Step 1: Find the initial vertical velocity (viy) and horizontal velocity (vix) components.
- The vertical component (viy) can be calculated using the initial speed and the angle of projection:
viy = vi * sin(θ)
- The horizontal component (vix) can be calculated using the initial speed and the angle of projection:
vix = vi * cos(θ)

Step 2: Find the time of flight (t) for the water stream to reach its maximum height.
- The time of flight is given by the following formula:
t = (2 * viy) / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).

Step 3: Find the horizontal distance (d) traveled by the water stream during the time of flight.
- The horizontal distance traveled is given by the formula:
d = vix * t

Let's calculate the values now:

Step 1:
viy = 20.1 m/s * sin(33.4°)
vix = 20.1 m/s * cos(33.4°)

Step 2:
t = (2 * viy) / g

Step 3:
d = vix * t

By following these steps and calculating the respective values, you will be able to find the horizontal distance at which the water should hit the highest possible fire.

v = Vi - 9.81 t

at top v = 0
t = Vi/9.81 at top

Vi = 20.1 sin 33.4 = 11.1
so t = 11.1/9.81 = 1.13 seconds at top

how far horizontal in 1.13 seconds?

u = 20.1 cos 33.4 = 16.8 m/s

16.8 m/s * 1.13 s = 19 meters