Final answer:
The additional time that elapses before the ball passes the tree branch on the way back down is approximately 1.53 seconds.
Step-by-step explanation:
To determine the additional time it takes for the ball to pass the tree branch on the way back down, we need to analyze the ball's motion. When the ball is thrown straight up, it reaches its highest point and then falls back down. The time it takes for the ball to reach the highest point is equal to the time it takes for the ball to fall back down.
So, the additional time elapsed before the ball passes the tree branch on the way back down is the same as the time it takes for the ball to reach the highest point.
The time it takes for an object to reach its highest point in projectile motion can be calculated using the formula:
t = (v - u) / g
Where t is the time, v is the final velocity, u is the initial velocity, and g is the acceleration due to gravity.
In this case, the initial velocity is 15.0 m/s, the final velocity is 0 (at the highest point), and the acceleration due to gravity is -9.8 m/s^2 (negative because it acts downward).
Plugging in these values, we have:
t = (0 - 15.0) / -9.8 = 1.53 s
Therefore, the additional time that elapses before the ball passes the tree branch on the way back down is approximately 1.53 seconds.