Final answer:
Using the vertical component of the football's initial velocity and the acceleration due to gravity, the time of flight can be calculated to be about 2.36 seconds, which is the time it takes for the football to hit the ground.
Step-by-step explanation:
The question is asking how long it takes for a football, kicked at an initial speed of 18.0 m/s at a 40.0-degree angle, to hit the ground. To solve this problem, we only need to consider the vertical motion since the football returns to the ground level, where it was kicked. The time of flight can be found using the kinematic equations for projectile motion.
First, we calculate the vertical component of the initial velocity using sin(θ) where θ is the angle of projection. Since the angle is 40 degrees, we have:
Vertical component = 18.0 m/s * sin(40°) ≈ 11.55 m/s
Using the kinematic equation v = u + at (where v is the final velocity, u is the initial velocity, a is the acceleration, and t is time) and knowing that at the peak of the trajectory the velocity will be 0 m/s, we can calculate the time to reach the peak:
0 = 11.55 m/s + (-9.81 m/s2) * t
t ≈ 1.18 s
Since the time to go up is the same as the time to come down, the total time of flight is:
Total time = 2 * 1.18 s ≈ 2.36 s
Therefore, the football will hit the ground approximately 2.36 seconds after being kicked.