Final answer:
To find out how long it takes for the pitcher's glove to return after being thrown up with an initial speed of 6.1 m/s, the total time for the round trip is approximately 1.244 seconds.
Step-by-step explanation:
To calculate the time it takes for the pitcher's glove to return to her after being thrown straight upward with an initial speed of 6.1 m/s, we can use the principles of physics related to vertical motion under the influence of gravity. Because the glove is projected upwards, it will eventually come to a stop before descending back down to the point of release. We can use the formula for the time to reach the maximum height t = v / g, where v is the initial speed and g is the acceleration due to gravity (approximately 9.8 m/s2). Therefore, time to reach the maximum height is t = 6.1 m/s / 9.8 m/s2 ≈ 0.622 s. Since the total time for the glove to return would be twice the time to reach the maximum height (upward and downward journey is symmetrical), the total time is 2 * 0.622 s ≈ 1.244 s.