Final answer:
The initial vertical velocity of the football at t=0 seconds is 4.90 m/s upward, based on the provided data point and understanding of linear motion in the context of projectile motion.
Step-by-step explanation:
To determine the initial vertical velocity of a football at t=0 sec using equations from linear motion, we need to analyze the motion described in the problem. According to the information provided, the vertical velocity of the football begins at 4.90 m/s during the time interval from 0 to 0.1 sec. Given that the graph of the ball's vertical velocity over time has a slope of -9.8 m/s2, which represents the acceleration due to gravity, we can infer that the initial vertical velocity is the same as the velocity at t=0.05 sec, since there is no significant change within such a short time frame. Therefore, the initial vertical velocity of the football is 4.90 m/s upward.