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Fire brigade man wants to extinguish a fire at a height of 6 m above the nozzle standing at a distance 5 m away from the fire. Find (1) the minimum velocity of the nozzle discharge required; (2) velocity of discharge if he could extinguish with angle of projection of 60°. [?
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Fire brigade man wants to extinguish a fire at a height of 6 m above t...
1. Minimum Velocity of the Nozzle Discharge Required
To find the minimum velocity of discharge from the nozzle, we can use the projectile motion principles. The fire brigade man needs to project water to a height of 6 m while standing 5 m away horizontally.
- Height (h): 6 m
- Horizontal Distance (d): 5 m
- Gravity (g): 9.81 m/s²
The vertical motion equation is:
- h = (v_y²) / (2g)
Where v_y is the vertical component of the velocity. The horizontal distance relates to the time 't' using:
- d = v_x * t
Where v_x is the horizontal component of the velocity. The resultant velocity (v) can be calculated as follows:
- Using the range formula, we find that the minimum velocity (v) needed can be found through:
v = sqrt((g * d²) / (2h))
Plugging in the values:
- v = sqrt((9.81 * 5²) / (2 * 6)) ≈ 8.2 m/s
2. Velocity of Discharge at an Angle of Projection of 60°
When the fire brigade man uses an angle of projection of 60°, the calculations change slightly as we need to consider both vertical and horizontal components of the velocity.
- Angle (θ): 60°
- Vertical Component (v_y): v * sin(θ)
- Horizontal Component (v_x): v * cos(θ)
Using the range formula for projectile motion:
- Horizontal distance (d) = (v² * sin(2θ)) / g
Substituting values:
- 5 = (v² * sin(120°)) / 9.81
Solving for 'v':
- v = sqrt((5 * 9.81) / (sin(120°))) ≈ 7.75 m/s
Conclusion
- Minimum Velocity: 8.2 m/s
- Velocity at 60°: 7.75 m/s
These calculations provide the necessary discharge velocities for effective firefighting efforts.
To find the minimum velocity of discharge from the nozzle, we can use the projectile motion principles. The fire brigade man needs to project water to a height of 6 m while standing 5 m away horizontally.
- Height (h): 6 m
- Horizontal Distance (d): 5 m
- Gravity (g): 9.81 m/s²
The vertical motion equation is:
- h = (v_y²) / (2g)
Where v_y is the vertical component of the velocity. The horizontal distance relates to the time 't' using:
- d = v_x * t
Where v_x is the horizontal component of the velocity. The resultant velocity (v) can be calculated as follows:
- Using the range formula, we find that the minimum velocity (v) needed can be found through:
v = sqrt((g * d²) / (2h))
Plugging in the values:
- v = sqrt((9.81 * 5²) / (2 * 6)) ≈ 8.2 m/s
2. Velocity of Discharge at an Angle of Projection of 60°
When the fire brigade man uses an angle of projection of 60°, the calculations change slightly as we need to consider both vertical and horizontal components of the velocity.
- Angle (θ): 60°
- Vertical Component (v_y): v * sin(θ)
- Horizontal Component (v_x): v * cos(θ)
Using the range formula for projectile motion:
- Horizontal distance (d) = (v² * sin(2θ)) / g
Substituting values:
- 5 = (v² * sin(120°)) / 9.81
Solving for 'v':
- v = sqrt((5 * 9.81) / (sin(120°))) ≈ 7.75 m/s
Conclusion
- Minimum Velocity: 8.2 m/s
- Velocity at 60°: 7.75 m/s
These calculations provide the necessary discharge velocities for effective firefighting efforts.
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Fire brigade man wants to extinguish a fire at a height of 6 m above the nozzle standing at a distance 5 m away from the fire. Find (1) the minimum velocity of the nozzle discharge required; (2) velocity of discharge if he could extinguish with angle of projection of 60°. [?
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Fire brigade man wants to extinguish a fire at a height of 6 m above the nozzle standing at a distance 5 m away from the fire. Find (1) the minimum velocity of the nozzle discharge required; (2) velocity of discharge if he could extinguish with angle of projection of 60°. [? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Fire brigade man wants to extinguish a fire at a height of 6 m above the nozzle standing at a distance 5 m away from the fire. Find (1) the minimum velocity of the nozzle discharge required; (2) velocity of discharge if he could extinguish with angle of projection of 60°. [? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Fire brigade man wants to extinguish a fire at a height of 6 m above the nozzle standing at a distance 5 m away from the fire. Find (1) the minimum velocity of the nozzle discharge required; (2) velocity of discharge if he could extinguish with angle of projection of 60°. [?.
Fire brigade man wants to extinguish a fire at a height of 6 m above the nozzle standing at a distance 5 m away from the fire. Find (1) the minimum velocity of the nozzle discharge required; (2) velocity of discharge if he could extinguish with angle of projection of 60°. [? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Fire brigade man wants to extinguish a fire at a height of 6 m above the nozzle standing at a distance 5 m away from the fire. Find (1) the minimum velocity of the nozzle discharge required; (2) velocity of discharge if he could extinguish with angle of projection of 60°. [? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Fire brigade man wants to extinguish a fire at a height of 6 m above the nozzle standing at a distance 5 m away from the fire. Find (1) the minimum velocity of the nozzle discharge required; (2) velocity of discharge if he could extinguish with angle of projection of 60°. [?.
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