Final answer:
The acceleration of the football while in the air can be determined using the equations of motion. The total time taken for the football to reach its peak and then come back down can be calculated using the equation for the time of flight for a projectile. Substituting the time back into the equation for vertical velocity, we can solve for the acceleration.
Step-by-step explanation:
The acceleration of the football while in the air can be determined using the equations of motion. In this case, since the initial vertical velocity of the football is +10 m/s, and assuming there is no air resistance, we can use the equation:
vf = vi + at
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity of the football when it hits the ground would be 0 m/s (since it will eventually come to a stop), and the initial velocity is +10 m/s. Therefore, the equation can be rearranged to solve for the acceleration:
0 = 10 + a * t
Since the football is thrown vertically and comes to a stop at its peak, we can assume the time taken to reach its peak is equal to the time taken to come back down. Therefore, the total time, t, would be the time taken to reach its peak and then reach the ground again. Using the equation for the time of flight for a projectile:
t = 2 * (initial vertical velocity) / (acceleration due to gravity)
where the acceleration due to gravity is approximately 9.8 m/s², we can substitute the given values and solve for t. Once we have t, we can substitute it back into the first equation to solve for the acceleration, a.