Physics Exam > Physics Questions > Maximum height reached by a rocket fired with...
Start Learning for Free
Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface is R/α. Find the value of α.
Correct answer is '3'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Maximum height reached by a rocket fired with a speed equal to 50% of ...
Applying energy conservation
The correct answer is: 3
Most Upvoted Answer
Maximum height reached by a rocket fired with a speed equal to 50% of ...
To calculate the maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth, we need to know the formula for escape velocity and the height equation for projectile motion.
The escape velocity from Earth can be calculated using the formula:
V_escape = sqrt((2 * G * M) / R)
Where:
- V_escape is the escape velocity
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Earth (approximately 5.972 × 10^24 kg)
- R is the radius of the Earth (approximately 6,371 km)
Substituting the known values:
V_escape = sqrt((2 * 6.67430 × 10^-11 * 5.972 × 10^24) / (6,371 × 10^3))
V_escape ≈ 11,186 m/s
To calculate the maximum height reached by the rocket fired with a speed equal to 50% of the escape velocity, we need to use the height equation for projectile motion:
h = (v^2 * sin^2θ) / (2g)
Where:
- h is the maximum height
- v is the initial velocity (50% of the escape velocity, so v = 0.5 * 11,186 m/s = 5,593 m/s)
- θ is the launch angle (we assume it to be 90° for maximum height)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the known values:
h = (5,593^2 * sin^2(90°)) / (2 * 9.8)
h ≈ (5,593^2 * 1) / 19.6
h ≈ 1,560,506 m
Therefore, the maximum height reached by the rocket is approximately 1,560,506 meters or 1,560.5 kilometers.
The escape velocity from Earth can be calculated using the formula:
V_escape = sqrt((2 * G * M) / R)
Where:
- V_escape is the escape velocity
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Earth (approximately 5.972 × 10^24 kg)
- R is the radius of the Earth (approximately 6,371 km)
Substituting the known values:
V_escape = sqrt((2 * 6.67430 × 10^-11 * 5.972 × 10^24) / (6,371 × 10^3))
V_escape ≈ 11,186 m/s
To calculate the maximum height reached by the rocket fired with a speed equal to 50% of the escape velocity, we need to use the height equation for projectile motion:
h = (v^2 * sin^2θ) / (2g)
Where:
- h is the maximum height
- v is the initial velocity (50% of the escape velocity, so v = 0.5 * 11,186 m/s = 5,593 m/s)
- θ is the launch angle (we assume it to be 90° for maximum height)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the known values:
h = (5,593^2 * sin^2(90°)) / (2 * 9.8)
h ≈ (5,593^2 * 1) / 19.6
h ≈ 1,560,506 m
Therefore, the maximum height reached by the rocket is approximately 1,560,506 meters or 1,560.5 kilometers.
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer?
Question Description
Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer?.
Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer?.
Solutions for Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer?, a detailed solution for Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? has been provided alongside types of Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface isR/α.Find the value ofα.Correct answer is '3'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics 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