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An aeroplane is flying with velocity 50√2 kilometre per hour in north east direction .wind is blowing at 25 km per hour from north to south what is the resultant displacement of aeroplane in 2 hours?
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An aeroplane is flying with velocity 50√2 kilometre per hour in north ...
**Resultant Displacement of the Aeroplane in 2 hours**
To find the resultant displacement of the aeroplane, we need to consider both the velocity of the plane and the wind speed.
Given data:
- Velocity of the plane = 50√2 km/h (north-east direction)
- Wind speed = 25 km/h (north to south)
To find the resultant displacement, we can break down the velocity of the plane into its components in the north and east directions.
Let's assume:
- Velocity of the plane in the north direction = V_n km/h
- Velocity of the plane in the east direction = V_e km/h
**Finding the Components of Plane's Velocity:**
Using trigonometry, we can find the values of V_n and V_e.
Given:
- Velocity of the plane = 50√2 km/h
- Angle between the velocity vector and the north direction = 45 degrees (since it is flying in the north-east direction)
Using the sine and cosine functions, we can find the components of the velocity:
- V_n = velocity of the plane * sin(angle)
= 50√2 * sin(45)
= 50 km/h
- V_e = velocity of the plane * cos(angle)
= 50√2 * cos(45)
= 50 km/h
So, the velocity of the plane can be broken down into V_n = 50 km/h (north) and V_e = 50 km/h (east).
**Effect of Wind on Plane's Velocity:**
The wind is blowing at a speed of 25 km/h from north to south. This means it will affect the plane's velocity in the north and east directions.
- In the north direction, the wind is blowing against the plane's velocity, so it will reduce the component of V_n by 25 km/h. Therefore, the new V_n component becomes V_n' = V_n - wind speed = 50 - 25 = 25 km/h (north).
- In the east direction, the wind is perpendicular to the plane's velocity, so it will not affect the component V_e. Therefore, the V_e component remains the same at 50 km/h (east).
**Calculating the Resultant Displacement:**
To find the resultant displacement, we need to calculate the total distance covered by the plane in 2 hours.
- Distance covered in the north direction = V_n' * time
= 25 km/h * 2 hours
= 50 km
- Distance covered in the east direction = V_e * time
= 50 km/h * 2 hours
= 100 km
Using the Pythagorean theorem, the resultant displacement can be calculated as:
Resultant displacement = √(Distance north)^2 + (Distance east)^2
= √(50 km)^2 + (100 km)^2
= √(2500 km^2 + 10000 km^2)
= √12500 km^2
= 111.8 km
Therefore, the resultant displacement of the aeroplane after 2 hours is approximately 111.8 km.
To find the resultant displacement of the aeroplane, we need to consider both the velocity of the plane and the wind speed.
Given data:
- Velocity of the plane = 50√2 km/h (north-east direction)
- Wind speed = 25 km/h (north to south)
To find the resultant displacement, we can break down the velocity of the plane into its components in the north and east directions.
Let's assume:
- Velocity of the plane in the north direction = V_n km/h
- Velocity of the plane in the east direction = V_e km/h
**Finding the Components of Plane's Velocity:**
Using trigonometry, we can find the values of V_n and V_e.
Given:
- Velocity of the plane = 50√2 km/h
- Angle between the velocity vector and the north direction = 45 degrees (since it is flying in the north-east direction)
Using the sine and cosine functions, we can find the components of the velocity:
- V_n = velocity of the plane * sin(angle)
= 50√2 * sin(45)
= 50 km/h
- V_e = velocity of the plane * cos(angle)
= 50√2 * cos(45)
= 50 km/h
So, the velocity of the plane can be broken down into V_n = 50 km/h (north) and V_e = 50 km/h (east).
**Effect of Wind on Plane's Velocity:**
The wind is blowing at a speed of 25 km/h from north to south. This means it will affect the plane's velocity in the north and east directions.
- In the north direction, the wind is blowing against the plane's velocity, so it will reduce the component of V_n by 25 km/h. Therefore, the new V_n component becomes V_n' = V_n - wind speed = 50 - 25 = 25 km/h (north).
- In the east direction, the wind is perpendicular to the plane's velocity, so it will not affect the component V_e. Therefore, the V_e component remains the same at 50 km/h (east).
**Calculating the Resultant Displacement:**
To find the resultant displacement, we need to calculate the total distance covered by the plane in 2 hours.
- Distance covered in the north direction = V_n' * time
= 25 km/h * 2 hours
= 50 km
- Distance covered in the east direction = V_e * time
= 50 km/h * 2 hours
= 100 km
Using the Pythagorean theorem, the resultant displacement can be calculated as:
Resultant displacement = √(Distance north)^2 + (Distance east)^2
= √(50 km)^2 + (100 km)^2
= √(2500 km^2 + 10000 km^2)
= √12500 km^2
= 111.8 km
Therefore, the resultant displacement of the aeroplane after 2 hours is approximately 111.8 km.
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An aeroplane is flying with velocity 50√2 kilometre per hour in north east direction .wind is blowing at 25 km per hour from north to south what is the resultant displacement of aeroplane in 2 hours?
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An aeroplane is flying with velocity 50√2 kilometre per hour in north east direction .wind is blowing at 25 km per hour from north to south what is the resultant displacement of aeroplane in 2 hours? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about An aeroplane is flying with velocity 50√2 kilometre per hour in north east direction .wind is blowing at 25 km per hour from north to south what is the resultant displacement of aeroplane in 2 hours? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aeroplane is flying with velocity 50√2 kilometre per hour in north east direction .wind is blowing at 25 km per hour from north to south what is the resultant displacement of aeroplane in 2 hours?.
An aeroplane is flying with velocity 50√2 kilometre per hour in north east direction .wind is blowing at 25 km per hour from north to south what is the resultant displacement of aeroplane in 2 hours? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about An aeroplane is flying with velocity 50√2 kilometre per hour in north east direction .wind is blowing at 25 km per hour from north to south what is the resultant displacement of aeroplane in 2 hours? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aeroplane is flying with velocity 50√2 kilometre per hour in north east direction .wind is blowing at 25 km per hour from north to south what is the resultant displacement of aeroplane in 2 hours?.
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