Projectile Motion: Calculating Initial Velocity of a Football

When discussing projectile motion, one of the key aspects to analyze is the initial velocity at which an object is launched. In this scenario, we are looking at a football being kicked a distance of 61.1 meters and traveling through the air for 4.82 seconds. To determine the initial velocity, we need to consider both the magnitude and direction of the velocity vector.

To begin our calculation, we first determine the horizontal component of the initial velocity (vx). This component remains constant throughout the motion as there are no external horizontal forces affecting it. By dividing the distance traveled (61.1 meters) by the time taken (4.82 seconds), we find that the horizontal velocity is approximately 12.67 m/s.

Given that the kick is at a launch angle of 45 degrees, the vertical component of the initial velocity (vy) is equal to the horizontal velocity (vx), resulting in vy ≈ 12.67 m/s. With these values, we can now determine the magnitude of the initial velocity using the Pythagorean theorem.

By applying the theorem and calculating the square root of the sum of the squares of vx and vy, we find that the magnitude of the initial velocity (v) is approximately 17.92 m/s. Furthermore, since the launch angle is at 45 degrees, the direction of the initial velocity is also 45 degrees above the horizontal.

Therefore, the football was kicked with an initial velocity of approximately 17.92 m/s at an angle of 45 degrees above the horizontal to cover a distance of 61.1 meters in the air for 4.82 seconds.