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A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 450 above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be________.
Correct answer is between '63.5,64'. Can you explain this answer?
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A fire hose nozzle directs a steady stream of water of velocity 50 m/s...
To find the maximum height reached by the stream of water, we can analyze the motion of the water using the principles of projectile motion. Projectile motion involves the motion of an object that is launched into the air and moves along a curved path under the influence of gravity.
Let's break down the problem into different components:
1. Initial Velocity:
The water is discharged from the fire hose nozzle with a velocity of 50 m/s at an angle of 45 degrees above the horizontal. To calculate the initial velocity components, we can use trigonometry:
Horizontal Component: Vx = V * cos(θ)
Vertical Component: Vy = V * sin(θ)
Given:
V = 50 m/s
θ = 45 degrees
Using the above equations, we can find the initial velocity components:
Vx = 50 * cos(45) = 35.35 m/s
Vy = 50 * sin(45) = 35.35 m/s
2. Time of Flight:
The time of flight is the total time taken by the water stream to reach the maximum height and then return to the ground. In projectile motion, the time of flight can be determined using the vertical component of velocity and the acceleration due to gravity.
Using the equation:
Vy = V0y + gt
Where:
V0y = initial vertical velocity component = Vy = 35.35 m/s
g = acceleration due to gravity = 9.81 m/s^2
t = time of flight (unknown)
At the maximum height, the vertical component of velocity becomes zero. So, we can rearrange the equation as follows:
0 = 35.35 - 9.81 * t
Solving for t, we get:
t = 35.35 / 9.81 = 3.60 s
3. Maximum Height:
To find the maximum height reached by the water stream, we can use the equation for the vertical displacement:
Δy = V0y * t - (1/2) * g * t^2
Where:
V0y = initial vertical velocity component = Vy = 35.35 m/s
t = time of flight = 3.60 s
g = acceleration due to gravity = 9.81 m/s^2
Substituting the values, we get:
Δy = 35.35 * 3.60 - (1/2) * 9.81 * (3.60)^2
= 127.26 - 63.00
= 64.26 m
Rounding off to two decimal places, the maximum height reached by the water stream above the hose nozzle is 64.00 m.
Therefore, the correct answer is between 63.5 m and 64 m.
Let's break down the problem into different components:
1. Initial Velocity:
The water is discharged from the fire hose nozzle with a velocity of 50 m/s at an angle of 45 degrees above the horizontal. To calculate the initial velocity components, we can use trigonometry:
Horizontal Component: Vx = V * cos(θ)
Vertical Component: Vy = V * sin(θ)
Given:
V = 50 m/s
θ = 45 degrees
Using the above equations, we can find the initial velocity components:
Vx = 50 * cos(45) = 35.35 m/s
Vy = 50 * sin(45) = 35.35 m/s
2. Time of Flight:
The time of flight is the total time taken by the water stream to reach the maximum height and then return to the ground. In projectile motion, the time of flight can be determined using the vertical component of velocity and the acceleration due to gravity.
Using the equation:
Vy = V0y + gt
Where:
V0y = initial vertical velocity component = Vy = 35.35 m/s
g = acceleration due to gravity = 9.81 m/s^2
t = time of flight (unknown)
At the maximum height, the vertical component of velocity becomes zero. So, we can rearrange the equation as follows:
0 = 35.35 - 9.81 * t
Solving for t, we get:
t = 35.35 / 9.81 = 3.60 s
3. Maximum Height:
To find the maximum height reached by the water stream, we can use the equation for the vertical displacement:
Δy = V0y * t - (1/2) * g * t^2
Where:
V0y = initial vertical velocity component = Vy = 35.35 m/s
t = time of flight = 3.60 s
g = acceleration due to gravity = 9.81 m/s^2
Substituting the values, we get:
Δy = 35.35 * 3.60 - (1/2) * 9.81 * (3.60)^2
= 127.26 - 63.00
= 64.26 m
Rounding off to two decimal places, the maximum height reached by the water stream above the hose nozzle is 64.00 m.
Therefore, the correct answer is between 63.5 m and 64 m.
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Community Answer
A fire hose nozzle directs a steady stream of water of velocity 50 m/s...
g = 9.81 m/sec2
At point A,
At point B, UBY = 0
Between A and B, (using equations Vy2 = uy2 + 2aysy in y direction)
H = 63.71m
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A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 450 above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be________.Correct answer is between '63.5,64'. Can you explain this answer?
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A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 450 above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be________.Correct answer is between '63.5,64'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 450 above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be________.Correct answer is between '63.5,64'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 450 above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be________.Correct answer is between '63.5,64'. Can you explain this answer?.
A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 450 above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be________.Correct answer is between '63.5,64'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 450 above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be________.Correct answer is between '63.5,64'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 450 above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be________.Correct answer is between '63.5,64'. Can you explain this answer?.
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