Goal Kick in soccer are a interruption in play where the goalie (or defender) is allowed to kick the ball free from pressure from 6 yards off of the goal line. On average, we can see goalies kick 60-70 yards. In this blog, I intend to find the characteristics of the average goal kick using physics. For the purpose of simplifying the calculations, we will assume air resistance is negligible, and the average angle of a goal kick is 45°. X Components: acceleration = 0 m/s^2 ΔX = 60, 65, and 70 horizontal velocity: V * cos(45°) Y Components: Acceleration due to Gravity: -9.8 m/s^2 Vertical Velocity: V * sin(45°) Due to the fact that there is no air resistance, the initial and final velocities are equal. This way we can use the Y components to solve for the balls time in flight vertically. Final Veloctiy = initial velocity + acceleration * time -V * sin(45) = V * sin(45) + (-9.8 m/s^2) * t -2 * V * sin(45) = -9.8 * t (-2 * v * 0.7) / -9.8 = t t = 0.14 * v By knowing the time, we can calculate the velocity of the ball using the x-components x = initial position * time + (0.5) * acceleration * time^2 60 = v * cos(45) * (0.14 * v) + (0.5) * (0) * (0.14 * v) 65 = v * cos(45) * (0.14 * v) + (0.5) * (0) * (0.14 * v) 70 = v * cos(45) * (0.14 * v) + (0.5) * (0) * (0.14 * v) 60 = v^2 * (0.098) 65 = v^2 * (0.098) 70 = v^2 * (0.098) V^2 = 612.245 V^2 = 663.265 V^2 = 714.286 V = 24.744 V = 25.754 V = 26.726 Average Velocity: 25.741 (24.744 + 25.754 + 26.726) / 3 = 25.741 Now that we know the average velocity of the range of distances, we can calculate the average time the ball spends in the air. t = 24.744 * (0.14) t = 25.754 * (0.14) t = 26.726 * (0.14) t = 3.46 t = 3.61 t = 3.74 Average Time: 3.60 (3.46 + 3.61 + 3.74) / 3 = 3.6033333 X - Velocity 25.741 * cos(45) = 13.522 m/s Balls Maximum Height
V final^2 = V initial^2 + 2(acceleration)(delta Y) 0 = 13.522 + (-9.8)(delta Y) Y = 21.78 m
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Below is an image of an intersection before and after construction.
The right turn radius was expanded to make right hand turns safer. This was especially helpful for the icy road conditions common here during the winter time. With icy roads, the cars had less friction but still attempted to go through the turn at the same speed, which led to many accidents. Now cars should be able to go through the turn at the posted speed limit and not fall into the path of any other cars. Post test, I am confident I did the best I could on the test, disregarding the fact that I feel I was not sufficiently prepared. Going into the test, I expected a lot harder of a challenge. Even though it was not as hard as I expected, it was still difficult. The challenges arose when work involved creating their own equations, because I haven't familiarized myself with the standard equations enough to recognize how to rearrange them. For future tests, I plan to dive deeper into the Mastering Physics assignments for review, along side re-reading class notes and notes provided.
So far I feel that physics has presented itself as a AP course should, fast and precise. I believe that from the work we have done so far that the class is manageable and that I am in the right place for this year. However, I am concerned about the workload to come. If it is anything like the 3 hours packet assigned to us the first week, I may be in over my head. Regardless, I am very excited to explore the world of physics for the first time with my wonderful teacher, Mr. Frost. He is passionate and intelligent and I really think I will learn a-lot from this course. For anyone who is thinking of taking this class, I can say so far the work has been worth the weight.
Till next time, peace out physics fam! |
AuthorMax Bloom - same dude who made this website so you should be familiar Archives
February 2019
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