Final answer:
To find the horizontal distance the football travels, we can use the equations of motion. By finding the time of flight using the vertical component of the initial velocity, we can then calculate the horizontal distance using the horizontal component of the initial velocity and the time of flight. The ball travels approximately 19.52 meters horizontally.
Step-by-step explanation:
To find the horizontal distance the football travels, we need to find the time of flight and then use it to calculate the horizontal distance.
The time of flight can be found using the vertical component of the initial velocity. When the ball reaches its maximum height, its vertical velocity will be zero. We can use the following equation:
Vf = Vi + a*t
Where:
Vf = final velocity (0 m/s)
Vi = initial velocity in the vertical direction (12 m/s)
a = acceleration in the vertical direction (-9.8 m/s²)
t = time of flight
By solving for t, we find that the time of flight is approximately 1.22 seconds.
The horizontal distance traveled can be found using the horizontal component of the initial velocity and the time of flight. We can use the following equation:
d = Vix * t
Where:
d = horizontal distance
Vix = initial velocity in the horizontal direction (16 m/s)
t = time of flight
By substituting the values, we have:
d = (16 m/s)(1.22 s) = 19.52 m
Therefore, the ball travels approximately 19.52 meters horizontally.