Final answer:
To determine the time a football remains in the air, its horizontal displacement, and maximum vertical displacement, we apply the kinematic equations to the given initial velocities in the vertical and horizontal directions.
Step-by-step explanation:
The student has asked about the time a football stays in the air, as well as its horizontal and maximum vertical displacements when kicked with an initial velocity. To solve this, we can use the kinematic equations of motion for projectile motion.
For calculating the time the football stays in the air, we'll focus on the vertical motion. The initial vertical velocity component is 19.0 m/s, and gravity acts downwards at 9.8 m/s2. The time (t) for the football to reach its highest point is when its vertical velocity becomes zero. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we calculate the time to reach the highest point. Since the motion is symmetrical, the total time in the air would be 2t.
To find the horizontal displacement, we use the equation s = vt, where s is the displacement, v is the velocity (15.0 m/s), and t is the total time the football stays in the air.
For the maximum vertical displacement (the maximum height), we use the equation s = ut + (1/2)at2, where u is the initial vertical velocity, a is acceleration due to gravity (negative in this case), and t is the time taken to reach the maximum height.