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kuruman said:
See also Winans Equations 20 - 27.Initial velocity and angle when a ball is kicked over a 3m fence
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SUMMARY
The discussion focuses on calculating the initial velocity and launch angle required for a ball to clear a 3-meter fence. The equations of motion used include horizontal and vertical components, specifically \(x = x_0 + v_{0,x}t\) and \(y = y_0 + v_{0,y}t - \frac{1}{2}gt^2\). The correct angle derived from the calculations is approximately \(58.3^\circ\) with an initial velocity of \(9.76 \, \text{m/s}\), contradicting the common assumption that \(45^\circ\) is optimal for maximum range. The discussion highlights the importance of verifying assumptions in physics problems.
PREREQUISITES- Understanding of projectile motion equations
- Familiarity with trigonometric functions such as sine and cosine
- Basic calculus for optimization techniques
- Knowledge of significant figures in scientific calculations
- Study the derivation of projectile motion equations in detail
- Learn about optimization techniques in calculus for minimizing initial velocity
- Explore the impact of launch angles on projectile trajectories
- Review the significance of significant figures in physics problems
Students in physics, particularly those studying mechanics, educators teaching projectile motion, and anyone involved in optimizing projectile trajectories in sports or engineering applications.
See also Winans Equations 20 - 27.- #62
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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.
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It most definitely is. Not to mention ##\vec{a}\times \vec{s} = \vec{v} \times \vec{u}## which I 'punt' whenever I can!kuruman said:
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