Assertion: The maximum horizontal range of projectile is proportional ...


when θ = 45º, R
max ∝ u
2

when θ = 90º, H
max ∝ u
2
It is clear that,

Assertion: The maximum horizontal range of projectile is proportional ...
Assertion: The maximum horizontal range of a projectile is proportional to the square of its velocity.
Reason: The maximum horizontal range of a projectile is equal to the maximum height attained by the projectile.
Explanation:
The assertion states that the maximum horizontal range of a projectile is proportional to the square of its velocity. Let's analyze this statement along with the reason provided.
1. Understanding Projectile Motion:
Projectile motion refers to the motion of an object that is launched into the air and moves along a curved path under the influence of gravity. It follows a parabolic trajectory.
2. Horizontal Range:
The horizontal range of a projectile is the maximum horizontal distance covered by the projectile before it hits the ground. It is an important parameter to consider when analyzing projectile motion.
3. Factors Affecting Horizontal Range:
The horizontal range of a projectile depends on various factors, including the initial velocity, launch angle, and acceleration due to gravity.
4. Velocity and Maximum Range:
The horizontal range of a projectile is directly affected by its initial velocity. The greater the initial velocity, the longer the projectile will stay in the air and the farther it will travel horizontally.
5. Relationship between Velocity and Range:
The horizontal range of a projectile is proportional to the square of its velocity. Mathematically, this relationship can be expressed as R ∝ v^2, where R represents the horizontal range and v represents the initial velocity.
6. Explanation of the Reason:
The reason provided states that the maximum horizontal range of a projectile is equal to the maximum height attained by the projectile. However, this is not correct. The maximum height attained by a projectile is determined by its launch angle and initial velocity, but it is not directly related to the horizontal range.
7. Conclusion:
Based on the above analysis, we can conclude that while the assertion is true, the reason provided is false. Therefore, option 'C' is the correct answer. The maximum horizontal range of a projectile is indeed proportional to the square of its velocity, but it is not equal to the maximum height attained by the projectile.