A firefighter located a distance of 15.5 meters from a burning building shoots a hose at an angle of 27 degrees above the horizontal. At what height above the hose nozzle does the water strike the building if
the initial speed of the stream is 39 meters per second?

To solve this problem, we need to break it into two components of motion: horizontal and vertical. We'll use the given initial velocity, angle, and distance to find the height where the water stream strikes the building.

### Step 1: Break the initial velocity into components
The initial velocity \( v_0 = 39 \, \text{m/s} \) is at an angle of \( \theta = 27^\circ \) above the horizontal. We can split this into horizontal (\( v_{0x} \)) and vertical (\( v_{0y} \)) components:
\[
v_{0x} = v_0 \cdot \cos(\theta)
\]
\[
v_{0y} = v_0 \cdot \sin(\theta)
\]
Substitute the known values:
\[
v_{0x} = 39 \cdot \cos(27^\circ)
\]
\[
v_{0y} = 39 \cdot \sin(27^\circ)
\]

### Step 2: Calculate the time it takes for the water to travel horizontally
The horizontal distance to the building is \( d_x = 15.5 \, \text{m} \), and since there is no horizontal acceleration (neglecting air resistance), the horizontal velocity remains constant. The time \( t \) to reach the building can be found using:
\[
t = \frac{d_x}{v_{0x}}
\]

### Step 3: Calculate the vertical displacement
Now, we can find the height where the water strikes the building using the equation for vertical motion:
\[
y = v_{0y} \cdot t - \frac{1}{2} g t^2
\]
where \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.

Now, let's calculate the values step by step.

I'll compute this for you.The height at which the water strikes the building is approximately \( 6.92 \, \text{meters} \) above the hose nozzle.

Would you like further details or explanations? Here are five related questions to consider:

1. How would a change in the angle affect the height and range of the water stream?
2. What would happen if the initial speed of the stream were increased?
3. How long does it take for the water to reach the building?
4. How does air resistance alter the trajectory of the water stream in real-life scenarios?
5. Can you derive the formula used to calculate the vertical height in projectile motion?

**Tip:** Always break down a projectile motion problem into horizontal and vertical components.

A firefighter located a distance of 15.5 meters from a burning building shoots a hose at an angle of 27 degrees above the horizontal. At what height above the hose nozzle does the water strike the building if the initial speed of the stream is 39 meters per second?

Solve a projectile motion problem where a firefighter, located 15.5 meters from a burning building, shoots a hose at a 27-degree angle with an initial speed of 39 m/s. Learn how to find the height at which the water strikes the building using kinematic equations. Suitable for Grades 10-12 students.

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