A fire hose ejects a stream of water at an angle of 32.2 ° above the horizontal. The water leaves the nozzle with a speed of 26.5 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?

Vo = 26.5m/s[32.2o].

Xo = 26.5*cos32.2 = 22.4 m/s.
Yo = 26.5*sin32.2 = 14.1 m/s

Y = Yo + g*Tr = 0 @ max. ht.
Tr = -Yo/g = -14.1/-9.8 = 1.44 s. =
Rise time.

D = Xo * Tr = 22.4m/s * 1.44s. = 32.3 m.

To determine the distance from the building where the fire hose should be located to hit the highest possible fire, we need to consider the motion of the water as a projectile.

First, we'll find the time it takes for the water to reach its maximum height. The vertical component of the initial velocity can be found using trigonometry:

Vy = V × sin(θ)
= 26.5 m/s × sin(32.2 °)
≈ 14.1 m/s

The time to reach the maximum height can be found using the equation:

Vy = Vy0 + a × t

Where Vy is the vertical component of velocity, Vy0 is the initial vertical velocity, a is the acceleration due to gravity (-9.8 m/s²), and t is the time.

0 = 14.1 m/s + (-9.8 m/s²) × t

Solving for t, we get:

t = 14.1 m/s ÷ 9.8 m/s²
≈ 1.44 s

The time to reach the maximum height is approximately 1.44 seconds.

Next, we'll find the maximum height the water reaches using the equation:

Δy = Vy0 × t + (1/2) × a × t²

Where Δy is the vertical displacement or height, Vy0 is the initial vertical velocity, a is the acceleration due to gravity (-9.8 m/s²), and t is the time.

Δy = 14.1 m/s × 1.44 s + (1/2) × (-9.8 m/s²) × (1.44 s)²

Δy ≈ 10.15 m

The water reaches a maximum height of approximately 10.15 meters.

Now, to find the horizontal distance (X) from the building, we'll use the equation:

X = V × cos(θ) × t

Where X is the horizontal distance, V is the initial velocity, θ is the launch angle, and t is the time.

X = 26.5 m/s × cos(32.2 °) × 1.44 s

X ≈ 30.42 m

Therefore, the fire hose should be located approximately 30.42 meters away from the building to hit the highest possible fire.