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A projectile is fired from the surface of the earth with a velocity of 5 ms–1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth.
The value of the acceleration due to gravity on the planet is (in ms–2) given g = 9.8 m/s2
- a)3.5
- b)5.9
- c)16.3
- d)110.8
Correct answer is option 'A'. Can you explain this answer?
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Given data:
- Initial velocity of projectile on Earth, \(u_{Earth} = 5 \, m/s\)
- Initial velocity of projectile on another planet, \(u_{planet} = 3 \, m/s\)
- Acceleration due to gravity on Earth, \(g_{Earth} = 9.8 \, m/s^2\)
Identical Trajectories:
- The trajectories of both projectiles are identical, meaning they follow the same path.
Formula for Projectile Motion:
- The horizontal and vertical motions of a projectile are independent of each other.
- The horizontal motion is uniform with no acceleration.
- The vertical motion is accelerated due to gravity.
Time of Flight:
- Time of flight for both projectiles is the same.
- Time of flight, \(T = \frac{2u_{y}}{g}\), where \(u_{y}\) is the vertical component of initial velocity.
Vertical Component of Initial Velocity:
- For Earth: \(u_{y_{Earth}} = 5 \, sin(\theta)\)
- For planet: \(u_{y_{planet}} = 3 \, sin(\theta)\)
Equating Time of Flight:
- \(\frac{2 \times 5 \times sin(\theta)}{9.8} = \frac{2 \times 3 \times sin(\theta)}{g_{planet}}\)
- Solving for \(g_{planet}\) gives \(g_{planet} = 3.5 \, m/s^2\)
Therefore, the acceleration due to gravity on the planet is approximately \(3.5 \, m/s^2\), which corresponds to option A.
- Initial velocity of projectile on Earth, \(u_{Earth} = 5 \, m/s\)
- Initial velocity of projectile on another planet, \(u_{planet} = 3 \, m/s\)
- Acceleration due to gravity on Earth, \(g_{Earth} = 9.8 \, m/s^2\)
Identical Trajectories:
- The trajectories of both projectiles are identical, meaning they follow the same path.
Formula for Projectile Motion:
- The horizontal and vertical motions of a projectile are independent of each other.
- The horizontal motion is uniform with no acceleration.
- The vertical motion is accelerated due to gravity.
Time of Flight:
- Time of flight for both projectiles is the same.
- Time of flight, \(T = \frac{2u_{y}}{g}\), where \(u_{y}\) is the vertical component of initial velocity.
Vertical Component of Initial Velocity:
- For Earth: \(u_{y_{Earth}} = 5 \, sin(\theta)\)
- For planet: \(u_{y_{planet}} = 3 \, sin(\theta)\)
Equating Time of Flight:
- \(\frac{2 \times 5 \times sin(\theta)}{9.8} = \frac{2 \times 3 \times sin(\theta)}{g_{planet}}\)
- Solving for \(g_{planet}\) gives \(g_{planet} = 3.5 \, m/s^2\)
Therefore, the acceleration due to gravity on the planet is approximately \(3.5 \, m/s^2\), which corresponds to option A.
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A projectile is fired from the surface of the earth with a velocity of 5 ms–1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth.The value of the acceleration due to gravity on the planet is (in ms–2) given g = 9.8 m/s2a)3.5b)5.9c)16.3d)110.8Correct answer is option 'A'. Can you explain this answer?
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A projectile is fired from the surface of the earth with a velocity of 5 ms–1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth.The value of the acceleration due to gravity on the planet is (in ms–2) given g = 9.8 m/s2a)3.5b)5.9c)16.3d)110.8Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A projectile is fired from the surface of the earth with a velocity of 5 ms–1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth.The value of the acceleration due to gravity on the planet is (in ms–2) given g = 9.8 m/s2a)3.5b)5.9c)16.3d)110.8Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is fired from the surface of the earth with a velocity of 5 ms–1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth.The value of the acceleration due to gravity on the planet is (in ms–2) given g = 9.8 m/s2a)3.5b)5.9c)16.3d)110.8Correct answer is option 'A'. Can you explain this answer?.
A projectile is fired from the surface of the earth with a velocity of 5 ms–1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth.The value of the acceleration due to gravity on the planet is (in ms–2) given g = 9.8 m/s2a)3.5b)5.9c)16.3d)110.8Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A projectile is fired from the surface of the earth with a velocity of 5 ms–1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth.The value of the acceleration due to gravity on the planet is (in ms–2) given g = 9.8 m/s2a)3.5b)5.9c)16.3d)110.8Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is fired from the surface of the earth with a velocity of 5 ms–1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth.The value of the acceleration due to gravity on the planet is (in ms–2) given g = 9.8 m/s2a)3.5b)5.9c)16.3d)110.8Correct answer is option 'A'. Can you explain this answer?.
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