Final answer:
To find the total time the ball was in the air, we calculate the time it takes to reach the maximum height with the given final velocity and then double it for the ascent and descent. The total time in the air is 11.72 s.
Step-by-step explanation:
The question involves calculating the total time a ball thrown straight up into the air remains in flight before it lands, with a final velocity just before landing given as -57.5 m/s. In physics, specifically kinematics, the motion of the ball is described by the equations of motion under constant acceleration due to gravity. Since the problem can be symmetrical, we can calculate the time taken to reach the highest point and then double it for the total flight time.
Using the equation v = u + at, where v is the final velocity, u is the initial velocity (which is zero at the highest point), a is the acceleration (which is -9.81 m/s2 because it's directed downwards), and t is the time. Substituting the given values and solving for t, we can find the time taken to fall from the highest point back to the original elevation. The initial velocity upwards would be equal in magnitude but opposite in direction to the final velocity. Therefore, t = -57.5 m/s / -9.81 m/s2 = 5.86 s, this gives us the time to reach the peak or come back down from it, so the total time in the air is 5.86 s * 2 = 11.72 s.