Projectile Motion: What Angle was the Ball Kicked at?

Explanation:

When a ball is kicked with an initial velocity of 68 m/s and takes 2.6 seconds to reach the apex, the angle at which it was kicked can be calculated using the principles of projectile motion in physics.

Projectile motion involves the motion of objects in a two-dimensional space under the influence of gravity. In this case, the vertical component of the ball's motion is of particular interest to determine the angle of kick.

The vertical velocity (Vy) of the ball can be expressed as Vy = V * sin(θ), where V is the initial launch velocity and θ is the angle of launch. Given that the ball takes 2.6 seconds to reach the apex, we can use this information to calculate the angle.

At the apex of the ball's trajectory, the velocity momentarily becomes zero due to the effect of gravity. By applying the equation Vf = Vi - g*t (where g is acceleration due to gravity, approximately 9.81 m/s²), we can find the initial vertical velocity component. This calculates to 25.5 m/s.

Substituting the values into the equation for Vy, we get 25.5 = 68 * sin(θ). By solving for θ using the inverse sine function, we find that the ball was kicked at an angle of approximately 22.2 degrees.

Understanding the physics of projectile motion and applying mathematical calculations can help determine important factors such as launch angle, velocity, and trajectory of objects in motion.