Initial velocity and angle when a ball is kicked over a 3m fence

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Homework Help Overview

The discussion revolves around determining the initial velocity and angle required for a ball to clear a 3-meter fence when kicked. The problem involves analyzing projectile motion, specifically focusing on the relationships between horizontal and vertical components of motion.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the equations of motion for projectile motion, questioning the validity of a 45-degree launch angle. Some express confusion over their calculations and the expected results, while others suggest that the angle may not be the only factor affecting the initial velocity.

Discussion Status

The conversation is ongoing, with participants sharing various interpretations of the problem. Some have offered insights into the nature of projectile motion and the implications of different angles on the initial velocity required to clear the fence. There is a recognition of the need to consider minimum velocity conditions, but no consensus has been reached on the correct approach or solution.

Contextual Notes

Participants note that the problem has been attempted by many students, leading to a belief that there should be a correct answer. There is also mention of potential discrepancies between individual calculations and expected results, raising questions about assumptions made in the problem setup.

  • #61
kuruman said:
This completes the condition for optimizing one of ##\Delta x##, ##\Delta y## or ##v_0## as the projection angle is varied:

"At optimization,(a) the projection velocity and the velocity at target are perpendicular and (b) the transit time is the same as if the projectile were dropped from rest a distance equal to the magnitude of the overall displacement vector."

I am amazed that there is still juice left to squeeze out of projectile motion.
👍 See also Winans Equations 20 - 27.
 
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  • #62
Instead of being amazed I should have reread Winans. Nevertheless, I think it's good to bring forth this simple statement of trajectory optimization. It is more likely to be noticed here than in a 1961 AJP article.
 
  • #63
kuruman said:
Instead of being amazed I should have reread Winans. Nevertheless, I think it's good to bring forth this simple statement of trajectory optimization. It is more likely to be noticed here than in a 1961 AJP article.
It most definitely is. Not to mention ##\vec{a}\times \vec{s} = \vec{v} \times \vec{u}## which I 'punt' whenever I can!
 
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