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A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is
- a)100 m
- b)80 m
- c)60 m
- d)50 m
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A cricketer can throw a ball to a maximum horizontal distance of 100 m...
Rmax = u2 / g = 100m (when θ= 45°)
∴ u2 = 100 × 10 = 1000
= 50 metre. (when θ= 90°)
∴ u2 = 100 × 10 = 1000
= 50 metre. (when θ= 90°)
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A cricketer can throw a ball to a maximum horizontal distance of 100 m...
Understanding the Problem
The problem states that a cricketer can throw a ball horizontally to a maximum distance of 100 m. We need to find the maximum height the ball can attain when thrown vertically with the same effort.
Key Concepts
- Projectile Motion: The ball thrown horizontally and vertically can be analyzed using the principles of projectile motion.
- Energy Conservation: The initial kinetic energy when throwing the ball is conserved in both horizontal and vertical throws.
Horizontal Throw
- When the ball is thrown horizontally, it covers a horizontal distance of 100 m.
- The range (horizontal distance) formula for projectile motion is given by R = (v^2 * sin(2θ)) / g, where θ is the angle of projection.
- For a horizontal throw, θ = 0°, which means the vertical component of velocity is zero.
Vertical Throw
- When throwing vertically, all the initial kinetic energy is converted into potential energy at the maximum height.
- The potential energy at height h is given by PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.
Energy Equivalence
- The kinetic energy when the ball is thrown horizontally can be equated to the potential energy at maximum height for the vertical throw.
- For the horizontal throw: KE = (1/2)mv^2.
- For the vertical throw: KE = mgh.
Calculating Maximum Height
- Since the range is 100 m, we can deduce the initial velocity (v) using the range formula.
- By conservation of energy and rearranging terms, for the vertical throw:
h = v^2 / (2g).
- Solving this gives us h = 50 m, which is the maximum height attained when thrown vertically.
Conclusion
- The maximum height attained by the ball when thrown vertically upwards with the same effort is 50 m (Option D).
The problem states that a cricketer can throw a ball horizontally to a maximum distance of 100 m. We need to find the maximum height the ball can attain when thrown vertically with the same effort.
Key Concepts
- Projectile Motion: The ball thrown horizontally and vertically can be analyzed using the principles of projectile motion.
- Energy Conservation: The initial kinetic energy when throwing the ball is conserved in both horizontal and vertical throws.
Horizontal Throw
- When the ball is thrown horizontally, it covers a horizontal distance of 100 m.
- The range (horizontal distance) formula for projectile motion is given by R = (v^2 * sin(2θ)) / g, where θ is the angle of projection.
- For a horizontal throw, θ = 0°, which means the vertical component of velocity is zero.
Vertical Throw
- When throwing vertically, all the initial kinetic energy is converted into potential energy at the maximum height.
- The potential energy at height h is given by PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.
Energy Equivalence
- The kinetic energy when the ball is thrown horizontally can be equated to the potential energy at maximum height for the vertical throw.
- For the horizontal throw: KE = (1/2)mv^2.
- For the vertical throw: KE = mgh.
Calculating Maximum Height
- Since the range is 100 m, we can deduce the initial velocity (v) using the range formula.
- By conservation of energy and rearranging terms, for the vertical throw:
h = v^2 / (2g).
- Solving this gives us h = 50 m, which is the maximum height attained when thrown vertically.
Conclusion
- The maximum height attained by the ball when thrown vertically upwards with the same effort is 50 m (Option D).
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Question Description
A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball isa)100 mb)80 mc)60 md)50 mCorrect answer is option 'D'. 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 cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball isa)100 mb)80 mc)60 md)50 mCorrect answer is option 'D'. 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 cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball isa)100 mb)80 mc)60 md)50 mCorrect answer is option 'D'. Can you explain this answer?.
A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball isa)100 mb)80 mc)60 md)50 mCorrect answer is option 'D'. 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 cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball isa)100 mb)80 mc)60 md)50 mCorrect answer is option 'D'. 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 cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball isa)100 mb)80 mc)60 md)50 mCorrect answer is option 'D'. Can you explain this answer?.
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