Final answer:
The initial horizontal velocity of the football is approximately 13.39 m/s and the initial vertical velocity is approximately 27.47 m/s.
Step-by-step explanation:
To determine the initial horizontal velocity (vx0) of the football, we can use the time it was in the air and the horizontal distance it traveled. Since the ball was caught at the same height it was kicked from and air resistance is ignored, the horizontal motion can be considered constant velocity motion. Therefore, we can calculate vx0 by dividing the distance by the time.
vx0 = distance / time
vx0 = 75 meters / 5.6 seconds
vx0 = approximately 13.39 meters per second (m/s)
To find the initial vertical velocity (vy0), we recognize that the total time of flight of the projectile is twice the time it takes to reach the maximum height (since the ascent and descent times are equal due to symmetry when the landing height is the same as the launch height). Hence, the time to reach the maximum height is 5.6 seconds / 2 = 2.8 seconds. Using the acceleration due to gravity (g = 9.81 m/s2), we can calculate vy0 by the formula vy0 = g x time.
vy0 = 9.81 m/s2 x 2.8 s
vy0 = approximately 27.47 m/s