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An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2) hours?
- a)300√67 km
- b)400√61 km
- c)200√61 km
- d)300√61 km
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
An aeroplane leaves an airport and flies due north at a speed of 1000 ...
Let the point A represent the airport.
Let the plane-I fly towards North.
∴ Distance of the plane-I from the airport after 1(1/2) hours
= Speed × Time = 1000 × (1)1/2 km= 1500 km
Let the plane-II fly towards West.
∴ Distance of the plane-II from the airport after (1)1/2 hours
= 1200 × (1)1/2km = 1800 km
Now, in right ∆ABC, using Pythagoras theorem, we have
BC2 = AB2 + AC2
⇒ BC2 = (1800)2 + (1500)2 = 5490000
⇒ BC =
Thus, after (1)1/2 hours, the two planes will be 300 √61 km apart from each other.
Let the plane-I fly towards North.
∴ Distance of the plane-I from the airport after 1(1/2) hours
= Speed × Time = 1000 × (1)1/2 km= 1500 km
Let the plane-II fly towards West.
∴ Distance of the plane-II from the airport after (1)1/2 hours
= 1200 × (1)1/2km = 1800 km
Now, in right ∆ABC, using Pythagoras theorem, we have
BC2 = AB2 + AC2
⇒ BC2 = (1800)2 + (1500)2 = 5490000
⇒ BC =
Thus, after (1)1/2 hours, the two planes will be 300 √61 km apart from each other.
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Community Answer
An aeroplane leaves an airport and flies due north at a speed of 1000 ...
Introduction
To determine the distance between the two planes after 1.5 hours, we will use the Pythagorean theorem, as they are flying at right angles to each other (one north and the other west).
Distance Calculations
- Plane 1 (North):
Speed = 1000 km/h
Time = 1.5 hours
Distance = Speed × Time = 1000 × 1.5 = 1500 km
- Plane 2 (West):
Speed = 1200 km/h
Time = 1.5 hours
Distance = Speed × Time = 1200 × 1.5 = 1800 km
Applying the Pythagorean Theorem
To find the distance between the two planes, we treat their paths as two sides of a right triangle:
- North Distance = 1500 km (Plane 1)
- West Distance = 1800 km (Plane 2)
The distance (D) between the two planes can be calculated as follows:
- D = √(North Distance² + West Distance²)
- D = √(1500² + 1800²)
Calculating the Squares
- 1500² = 2250000
- 1800² = 3240000
Now, add these values:
- Total = 2250000 + 3240000 = 5490000
Final Calculation
- D = √5490000
- D = √(1000² × 61) = 1000√61
Thus, the distance between the two planes after 1.5 hours is 300√61 km.
Conclusion
Therefore, the correct answer is option D) 300√61 km.
To determine the distance between the two planes after 1.5 hours, we will use the Pythagorean theorem, as they are flying at right angles to each other (one north and the other west).
Distance Calculations
- Plane 1 (North):
Speed = 1000 km/h
Time = 1.5 hours
Distance = Speed × Time = 1000 × 1.5 = 1500 km
- Plane 2 (West):
Speed = 1200 km/h
Time = 1.5 hours
Distance = Speed × Time = 1200 × 1.5 = 1800 km
Applying the Pythagorean Theorem
To find the distance between the two planes, we treat their paths as two sides of a right triangle:
- North Distance = 1500 km (Plane 1)
- West Distance = 1800 km (Plane 2)
The distance (D) between the two planes can be calculated as follows:
- D = √(North Distance² + West Distance²)
- D = √(1500² + 1800²)
Calculating the Squares
- 1500² = 2250000
- 1800² = 3240000
Now, add these values:
- Total = 2250000 + 3240000 = 5490000
Final Calculation
- D = √5490000
- D = √(1000² × 61) = 1000√61
Thus, the distance between the two planes after 1.5 hours is 300√61 km.
Conclusion
Therefore, the correct answer is option D) 300√61 km.
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An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer?.
An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer?.
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An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1(1/2)hours?a)300√67 kmb)400√61 kmc)200√61 kmd)300√61 kmCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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