Final answer:
To find the speed at which the ball hits the floor, you can use the equation v^2 = u^2 + 2as where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. Substituting the given values into the equation, you can solve for v.
Step-by-step explanation:
To find the speed at which the ball hits the floor, we need to consider the vertical component of its motion. The ball is initially kicked with a vertical velocity of 12 m/s. Assuming no air resistance, the ball will continue to accelerate downwards due to gravity at a rate of 9.8 m/s^2. We can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. In this case, the final velocity is 0 m/s since the ball hits the floor, the initial velocity is 12 m/s (assuming upward is positive), and the acceleration is -9.8 m/s^2 (since gravity pulls the ball downward). The displacement, s, is the height from which the ball is dropped. Therefore, we can substitute these values into the equation and solve for v.
v^2 = 12^2 + 2(-9.8)s
0 = 144 - 19.6s
19.6s = 144
s = 144 / 19.6
s ≈ 7.35
So, the ball hits the floor with a speed of approximately 7.35 m/s.