Final answer:
The problem requires applying the kinematic equations of projectile motion to determine the speed upon impact, total time airborne, and maximum height. Horizontal and vertical motions are analyzed independently to find each answer.
Step-by-step explanation:
The question concerns a ball kicked at an initial velocity with both horizontal and vertical components. We will utilize the kinematic equations of projectile motion to solve for the speed when the ball hits the ground, the time the ball remains in the air, and the maximum height attained by the ball. It's important to consider each component of the motion separately, as horizontal and vertical motions are independent in projectile motion under uniform gravity and with no air resistance.
Speed when the ball hits the ground:
To determine the speed when the ball hits the ground, we use the Pythagorean theorem, considering both the horizontal and vertical components of velocity at the moment of impact. Since there's no air resistance, the horizontal velocity (16 m/s) remains constant during the projectile's flight. The vertical component of the velocity just before the ball hits the ground can be found by using the kinematic equation v = u + at, where 'u' is the initial vertical velocity (12 m/s), 'a' is the acceleration due to gravity (-9.81 m/s2 since it is in the opposite direction of the initial vertical velocity), and 't' is the total time in the air.
Time in the air:
The time the ball remains in the air is calculated using the vertical component of the projectile's motion. Since the ball returns to the same vertical level from which it was kicked, we can use the equation of motion h = ut + 0.5at2 to solve for 't', where 'h' equals zero for the round trip.
Maximum height attained by the ball:
To find the maximum height, we consider that at the peak of its flight, the vertical velocity will be zero. Using the kinematic equation v2 = u2 + 2ah, where 'v' is zero at the maximum height, we can solve for 'h'.