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A man is climbing a ladder which is inclined at the wall at angle of 30 degree if he essence at the rate of 2 m per second then a process the wall at the rate of?
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A man is climbing a ladder which is inclined at the wall at angle of 3...
Understanding the Problem
In this scenario, a man is climbing a ladder that is inclined at a 30-degree angle to the wall. He ascends the ladder at a speed of 2 m/s. Our goal is to determine the rate at which he is approaching the wall.
Key Concepts
- Inclined Ladder: The ladder forms a right triangle with the wall and the ground.
- Angle of Inclination: The ladder makes a 30-degree angle with the horizontal ground.
Calculating the Vertical and Horizontal Components
When the man climbs the ladder, his movement can be broken down into vertical and horizontal components using trigonometry.
- Vertical Speed: The vertical speed (height gain) can be calculated using the sine of the angle.
- Horizontal Speed: The horizontal speed (distance towards the wall) uses the cosine of the angle.
Formulas to Use
- Vertical Speed (Vv) = Climbing Speed * sin(30 degrees)
- Horizontal Speed (Vh) = Climbing Speed * cos(30 degrees)
Since sin(30 degrees) = 1/2 and cos(30 degrees) = √3/2:
- Vertical Speed (Vv) = 2 m/s * 1/2 = 1 m/s
- Horizontal Speed (Vh) = 2 m/s * √3/2 ≈ 1.732 m/s
Rate Approaching the Wall
The horizontal speed indicates how quickly the man is approaching the wall:
- Rate of Approaching the Wall: Approximately 1.732 m/s
Conclusion
As the man climbs the ladder, he approaches the wall at a rate of approximately 1.732 meters per second. Understanding these components is essential for solving similar problems in geometry and physics.
In this scenario, a man is climbing a ladder that is inclined at a 30-degree angle to the wall. He ascends the ladder at a speed of 2 m/s. Our goal is to determine the rate at which he is approaching the wall.
Key Concepts
- Inclined Ladder: The ladder forms a right triangle with the wall and the ground.
- Angle of Inclination: The ladder makes a 30-degree angle with the horizontal ground.
Calculating the Vertical and Horizontal Components
When the man climbs the ladder, his movement can be broken down into vertical and horizontal components using trigonometry.
- Vertical Speed: The vertical speed (height gain) can be calculated using the sine of the angle.
- Horizontal Speed: The horizontal speed (distance towards the wall) uses the cosine of the angle.
Formulas to Use
- Vertical Speed (Vv) = Climbing Speed * sin(30 degrees)
- Horizontal Speed (Vh) = Climbing Speed * cos(30 degrees)
Since sin(30 degrees) = 1/2 and cos(30 degrees) = √3/2:
- Vertical Speed (Vv) = 2 m/s * 1/2 = 1 m/s
- Horizontal Speed (Vh) = 2 m/s * √3/2 ≈ 1.732 m/s
Rate Approaching the Wall
The horizontal speed indicates how quickly the man is approaching the wall:
- Rate of Approaching the Wall: Approximately 1.732 m/s
Conclusion
As the man climbs the ladder, he approaches the wall at a rate of approximately 1.732 meters per second. Understanding these components is essential for solving similar problems in geometry and physics.
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A man is climbing a ladder which is inclined at the wall at angle of 30 degree if he essence at the rate of 2 m per second then a process the wall at the rate of?
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A man is climbing a ladder which is inclined at the wall at angle of 30 degree if he essence at the rate of 2 m per second then a process the wall at the rate of? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A man is climbing a ladder which is inclined at the wall at angle of 30 degree if he essence at the rate of 2 m per second then a process the wall at the rate of? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is climbing a ladder which is inclined at the wall at angle of 30 degree if he essence at the rate of 2 m per second then a process the wall at the rate of?.
A man is climbing a ladder which is inclined at the wall at angle of 30 degree if he essence at the rate of 2 m per second then a process the wall at the rate of? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A man is climbing a ladder which is inclined at the wall at angle of 30 degree if he essence at the rate of 2 m per second then a process the wall at the rate of? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is climbing a ladder which is inclined at the wall at angle of 30 degree if he essence at the rate of 2 m per second then a process the wall at the rate of?.
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