Final answer:
To calculate the time of flight for a ball thrown vertically upward with an initial speed of 15 m/s, we can use the physics formula for vertical motion under gravity. After finding the time to reach the highest point (about 1.53 seconds), we double this to get the total time of flight (about 3.06 seconds).
Step-by-step explanation:
To determine the time of flight for a ball thrown vertically upward with a speed of 15 m/s that returns to its original position, we can use the following physics concept. The entire motion is symmetric, meaning that the time it takes for the ball to reach its highest point is the same as the time it takes to fall back down from that point to the launch position. The acceleration due to gravity (g) is approximately 9.81 m/s2, and it acts downwards. At the highest point, the ball's velocity will be 0 m/s.
The formula to use is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (which will be -9.81 m/s2 because gravity is acting in the opposite direction to the ball's motion), and t is the time. Solving for t when v is 0 m/s gives us:
0 = 15 m/s - (9.81 m/s2 × t)
This can be rearranged to find the time to the top of the motion:
t = 15 m/s / 9.81 m/s2
The time it takes to reach the highest point is approximately 1.53 seconds. Since the time up equals the time down, the total time of flight is twice this, so approximately 3.06 seconds.