Final answer:
To determine the time in the air, range, and maximum height of the kicked soccer ball, we use projectile motion equations separating motion into horizontal and vertical components.
Step-by-step explanation:
To solve for the time the ball is in the air (total time of flight), as well as how far away it lands (range), and how high it travels (maximum height), we can use the equations of projectile motion. Assuming no air resistance, the problem can be separated into horizontal and vertical components.
(a) The time a projectile is in the air is determined by its initial vertical velocity and the acceleration due to gravity. The formula used is t = (2 * v * sin(θ)) / g, where v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (9.8 m/s2).
(b) The range of the projectile is found using the formula R = v2 * sin(2θ) / g. This equation finds the horizontal distance the projectile will travel.
(c) The maximum height is calculated using the formula H = (v2 * sin2(θ)) / (2 * g), where only the vertical component of the velocity (v * sin(θ)) is used because it affects how high the ball goes.