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
0 Comments
Leave a Reply. |
AuthorMax Bloom - same dude who made this website so you should be familiar Archives
February 2019
Categories |