When analyzing the trajectories of kicked footballs, it's essential to understand how the initial vertical and horizontal velocity components affect the time of flight. Let's break down the problem step by step to determine which statement from Column 2 corresponds correctly to the variables in Column 1.
Understanding the Components of Motion
In projectile motion, the time of flight depends primarily on the vertical component of the initial velocity (Uy). The horizontal component (Ux) influences how far the projectile travels horizontally but does not affect the time it spends in the air, assuming we ignore air resistance.
Key Factors Affecting Time of Flight
- Vertical Velocity (Uy): The greater the initial vertical velocity, the longer the projectile will stay in the air.
- Horizontal Velocity (Ux): While it determines the range, it does not impact the time of flight directly.
Analyzing the Options
Now, let's evaluate the statements in Column 2 based on the information about the trajectories of the three footballs (A, B, and C).
Evaluating Each Statement
- Statement a: "greatest for A only Uy/Ux" - This suggests that football A has the highest ratio of vertical to horizontal velocity, leading to the longest time of flight.
- Statement b: "greatest for C only Ux" - This implies that football C has the highest horizontal velocity, which does not affect the time of flight.
- Statement c: "equal for A and B UxUy" - This indicates that both A and B have the same product of their velocities, which could lead to equal time of flight if their vertical components are similar.
- Statement d: "equal for B and C" - This suggests that B and C have the same time of flight, which would only be true if their vertical components were equal.
Determining the Correct Statement
To find the correct statement, we need to focus on the vertical components of the velocities (Uy) since they dictate the time of flight. If we assume that:
Football A has the highest vertical velocity, it will have the longest time of flight.
Football B has a moderate vertical velocity.
Football C has the lowest vertical velocity.
In this scenario, the correct statement would be that the time of flight is greatest for A only, which aligns with statement a. Therefore, the answer is:
Time of flight is greatest for A only (Statement a).
Conclusion
In summary, when analyzing the time of flight for projectiles, always focus on the vertical component of the initial velocity. The horizontal component, while important for determining range, does not influence how long the projectile remains airborne. This understanding is crucial for solving similar problems in projectile motion.
