Class 10 Exam > Class 10 Questions > The angle of elevation of an aeroplane from t...
Start Learning for Free
The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying?
Most Upvoted Answer
The angle of elevation of an aeroplane from the point on on the ground...
Problem: The angle of elevation of an aeroplane from a point on the ground is 60 degrees after a flight of 10 seconds. On the same height, the angle of elevation from another point becomes 30 degrees. If the aeroplane is flying at the speed of 720 kilometers, find the constant height at which the aeroplane is flying.
Solution:
Let us assume that the height of the aeroplane from the ground is h.
Step 1: Finding the distance travelled by the plane in 10 seconds.
We know that the plane is flying at a speed of 720 km/hr.
Therefore, the distance travelled in 10 seconds is:
720 km/hr = (720 x 1000) m/hr [Converting km/hr to m/hr]
= (720 x 1000) / 3600 m/s [Converting m/hr to m/s]
= 200 m/s
So, the distance travelled by the plane in 10 seconds is:
Distance = Speed x Time
= 200 m/s x 10 s
= 2000 m
Step 2: Finding the horizontal distance of the plane from the two points.
Let us assume that the distance of the plane from the first point is x.
Then, the distance of the plane from the second point is (2000 - x) [As the plane is flying at a constant height h]
Step 3: Finding the height of the plane.
We know that the angle of elevation from the first point is 60 degrees.
Therefore, we can write:
tan 60 = h/x
√3 = h/x
h = √3 x
Similarly, the angle of elevation from the second point is 30 degrees.
Therefore, we can write:
tan 30 = h/(2000 - x)
1/√3 = h/(2000 - x)
h = (2000 - x)/√3
Step 4: Equating the two expressions for height.
As the height of the plane is constant, we can equate the two expressions for height obtained in Step 3.
√3 x = (2000 - x)/√3
On solving, we get:
x = 500√3
h = 500
Therefore, the constant height at which the plane is flying is 500 meters.
Solution:
Let us assume that the height of the aeroplane from the ground is h.
Step 1: Finding the distance travelled by the plane in 10 seconds.
We know that the plane is flying at a speed of 720 km/hr.
Therefore, the distance travelled in 10 seconds is:
720 km/hr = (720 x 1000) m/hr [Converting km/hr to m/hr]
= (720 x 1000) / 3600 m/s [Converting m/hr to m/s]
= 200 m/s
So, the distance travelled by the plane in 10 seconds is:
Distance = Speed x Time
= 200 m/s x 10 s
= 2000 m
Step 2: Finding the horizontal distance of the plane from the two points.
Let us assume that the distance of the plane from the first point is x.
Then, the distance of the plane from the second point is (2000 - x) [As the plane is flying at a constant height h]
Step 3: Finding the height of the plane.
We know that the angle of elevation from the first point is 60 degrees.
Therefore, we can write:
tan 60 = h/x
√3 = h/x
h = √3 x
Similarly, the angle of elevation from the second point is 30 degrees.
Therefore, we can write:
tan 30 = h/(2000 - x)
1/√3 = h/(2000 - x)
h = (2000 - x)/√3
Step 4: Equating the two expressions for height.
As the height of the plane is constant, we can equate the two expressions for height obtained in Step 3.
√3 x = (2000 - x)/√3
On solving, we get:
x = 500√3
h = 500
Therefore, the constant height at which the plane is flying is 500 meters.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying?
Question Description
The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? 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 The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying?.
The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? 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 The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying?.
Solutions for The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? defined & explained in the simplest way possible. Besides giving the explanation of
The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying?, a detailed solution for The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? has been provided alongside types of The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? theory, EduRev gives you an
ample number of questions to practice The angle of elevation of an aeroplane from the point on on the ground is 60 degree after a flight of 10 second on the same height the angle of elevation from a point become 30 degree if the aeroplane is flying at the speed of 720 kilometre find the constant height of at which the aeroplane is flying? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup