A fire hose ejects a stream of water at an angle of 38.3 ° above the horizontal. The water leaves the nozzle with a speed of 29.5 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 = 29.5 m/s @ 38.3 Deg.

Xo = 29.5*cos38.3 = 23.2 m/s.
Yo = 29.5*sin38.3 = 18.3 m/s.

Tr = (Yf-Yo)/g,
Tr = ( 0-18.3) / -9.8 = 1.87 s = Rise
time or time to reach max ht.

Dx = X0 * Tr = 23.2m/s * 1.87s =43.4 m.
= Dist from bldg.

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

First, we can analyze the vertical motion of the water stream. The initial vertical velocity can be determined using the given speed and the angle with the horizontal. We can use trigonometry to find the vertical component of the velocity:

Vertical component of velocity (Vy) = Speed × sin(angle)
= 29.5 m/s × sin(38.3°)

Next, we can determine the time it takes for the water stream to reach its maximum height. At the highest point, the vertical velocity becomes zero. We can use the equation of motion for vertical projectile motion:

Vy = Vo + gt

Substituting the values, where g is the acceleration due to gravity (-9.8 m/s²):

0 = Vy + (-9.8 m/s²) × t

Solving for t, we can find the time it takes for the water stream to reach its highest point.

Once we have the time, we can determine the horizontal distance traveled by the water stream. The horizontal distance is given by:

Horizontal distance = Speed × cos(angle) × time

Substituting the values, we can calculate the distance.

So, by performing these calculations, we can determine how far from the building the fire hose should be located to hit the highest possible fire.