A firefighter 41.8m away from a burning building, directs Zach stream of water from a ground level fire hose at an angle of 33.0 degrees above the horizontal . If the speed of the streams it leaves the hose is 42.7m/s, at what height will the stream of water hit the building

Vo = 42.7m/s[33o]

Xo = 42.7*cos33 = 35.81 m/s.
Yo = 42.7*sin33 = 23.26 m/s.

X = Xo * t = 41.8 m.
35.81t = 41.8
t = 1.17 s

h = Yo*t - 4.9*t^2
h = 23.26*1.17 - 4.9*1.17^2 = 20.51 m.

To find the height at which the stream of water hits the building, we need to determine the vertical component of the stream's velocity.

First, let's break down the given information:

- Distance from the firefighter to the building (horizontal distance): 41.8m
- Angle between the stream of water and the horizontal: 33.0 degrees
- Speed of the stream of water: 42.7m/s

Now, we can calculate the vertical component of the stream's velocity using trigonometry.

The vertical component of the velocity (Vy) can be found using the equation:

Vy = V * sin(θ)

where V is the speed of the stream of water and θ is the angle above the horizontal.

Plugging in the values, we have:

Vy = 42.7m/s * sin(33.0 degrees)

Now, calculate the value of sin(33.0 degrees):

sin(33.0 degrees) ≈ 0.544

Vy = 42.7m/s * 0.544

Vy ≈ 23.2112 m/s

So, the vertical component of the velocity is approximately 23.2112 m/s.

Next, we can determine the time it takes for the stream of water to reach the building.

We know the horizontal distance (41.8m) and the horizontal component of the velocity (Vx) can be found using the equation:

Vx = V * cos(θ)

Using the given information:

Vx = 42.7m/s * cos(33.0 degrees)

Now, calculate the value of cos(33.0 degrees):

cos(33.0 degrees) ≈ 0.836

Vx = 42.7m/s * 0.836

Vx ≈ 35.6764 m/s

So, the horizontal component of the velocity is approximately 35.6764 m/s.

To calculate the time (t), we can use the formula:

t = d / Vx

where d is the horizontal distance.

Plugging in the values:

t = 41.8m / 35.6764 m/s

t ≈ 1.1708 s

Therefore, it takes approximately 1.1708 seconds for the stream of water to reach the building.

Finally, we can calculate the height (h) using the formula:

h = Vy * t

Plugging in the values:

h ≈ 23.2112 m/s * 1.1708 s

h ≈ 27.1341 m

Therefore, the stream of water will hit the building at a height of approximately 27.1341 meters.