AIIMS 2019 Physics Range and Time of Flight MCQ Question
The maximum range of projectile motion is given as, R = u² sin 2θ / g. The time of flight of projectile motion is given as, T = 2u sin θ / g. The square of time of flight of projectile motion is, T² = (2u sin θ / g)² = 4u² sin² θ / g². The ratio of maximum range and square of time of flight in projectile motion is calculated as, R / T² = (u² sin 2θ / g) / (4u² sin² θ / g²) = g / 2 cot θ.
Correct Answer
Detailed Explanation
The ratio of maximum range to the square of the time of flight in projectile motion simplifies to , demonstrating the relationship between these two parameters. This result is derived from substituting the formulas for and into the ratio, confirming that it holds true for any angle . Since option A is the only one provided, it is deemed correct, while other options are not applicable or relevant in this context. Understanding this ratio helps in analyzing projectile motion and its dependence on launch angle and initial velocity.
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