A Reflective Analysis on the Motion of a Football in Physics

How can we determine the position of a football 1.2 seconds after it is kicked?

Given the initial velocity of the football and the angle of projection, what are the horizontal and vertical components of its motion after 1.2 seconds?

Analysis of the Football's Motion 1.2 Seconds After Being Kicked

After kicking the ball with an initial velocity of 25 m/s at an angle of 30° to the horizontal, we need to analyze its horizontal and vertical motion separately to determine its position after 1.2 seconds.

To calculate the horizontal displacement of the football, we first find the horizontal velocity component using trigonometry:

Horizontal component (Vx) = Initial velocity (25 m/s) * cos(30°)

By substituting the values, we get Vx = 25 m/s * cos(30°) = 25 * (√3)/2 ≈ 21.65 m/s

Next, we calculate the horizontal displacement using the formula:

Horizontal displacement (dx) = Horizontal velocity component * time

Substituting the values, dx = 21.65 m/s * 1.2 s ≈ 25.98 meters

For the vertical motion, the initial vertical velocity is found using:

Vertical component (Vy) = Initial velocity (25 m/s) * sin(30°)

By calculating, Vy = 25 m/s * sin(30°) = 25 * 0.5 = 12.5 m/s

Then, we compute the vertical displacement with the equation:

Vertical displacement (dy) = Vertical velocity * time + 0.5 * acceleration due to gravity * time^2

Substituting the values, dy = 12.5 m/s * 1.2 s + 0.5 * 9.8 m/s^2 * (1.2 s)^2 ≈ 22.056 meters

Combining the horizontal and vertical displacements using the Pythagorean theorem, we find the overall displacement:

Overall displacement = √(Horizontal displacement^2 + Vertical displacement^2)

By calculating, d = √((25.98 m)^2 + (22.056 m)^2) ≈ √1160.58 m^2 ≈ 34.05 meters

Therefore, the football will be approximately 34.05 meters away from the point of kick after 1.2 seconds. This analysis demonstrates how we can determine the position of a moving object using principles of physics.