A fire hose ejects a stream of water at an angle of 37.8 ° 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?
time of max water height is ... [20.1 * sin(37.8º)] / 9.8
distance is ... (max time) * [20.1 * sin(37.8º)]
Vo = 20.1m/s[37.8o],
Xo = 20.1*Cos37.8 = 15.88 m/s. = Hor. component of Vo.
Yo = Vo*sin37.8 = 20.1*sin37.8 = 12.32 m/s. = Ver. component of Vo.
Y = Yo + g*Tr = 0 at max. ht.
12.32 - 9.8*Tr = 0,
Tr = 1.26 s. = Rise time.
d = Xo*Tr = 15.88 * 1.26 = 20.0 m. from a building.
To find the distance from the building where the fire hose should be located to hit the highest possible fire, we can use the principles of projectile motion.
First, let's break down the motion into horizontal and vertical components:
1. Horizontal Motion:
The horizontal component of the water's velocity remains constant throughout the motion. Therefore, the horizontal distance traveled by the water is directly proportional to the time of flight. The time of flight can be determined using the formula:
time = (2 * V₀ * sin(θ)) / g
where V₀ is the initial velocity (20.1 m/s) and θ is the angle of projection (37.8 °).
Plugging in the values, we get:
time = (2 * 20.1 * sin(37.8)) / 9.8
2. Vertical Motion:
The vertical component of the water's velocity changes due to gravity. The maximum height reached by the water can be calculated using the formula:
max height = (V₀² * sin²(θ)) / (2 * g)
Plugging in the values, we get:
max height = (20.1² * sin²(37.8)) / (2 * 9.8)
Now, to find the horizontal distance from the building, we need to calculate the horizontal displacement. The horizontal displacement is given by:
horizontal displacement = horizontal velocity * time
The horizontal velocity can be calculated using the formula:
horizontal velocity = V₀ * cos(θ)
Plugging in the values, we have:
horizontal displacement = (20.1 * cos(37.8)) * time
Putting it all together, we can find the distance from the building where the fire hose should be located by calculating the horizontal displacement.