Final answer:
The additional time before the ball passes the tree branch on the way back down can be calculated using kinematic equations and considering the initial velocity and acceleration due to gravity.
Step-by-step explanation:
The question concerns the dynamics of a ball being thrown upwards and later falling back passing the same reference point, which is a tree branch at a height of 7.00 m.
To solve the question, we need to apply the kinematic equations for uniformly accelerated motion with the acceleration due to gravity.
The ball is thrown with an initial velocity of 15.0 m/s and the acceleration acting on it is -9.8 m/s2 (negative because it acts downward).
The additional time it will take for the ball to pass the tree branch on its way back down can be found by calculating the time it takes to reach the maximum height and then the time to descend back to the height of the branch.
Step-by-step solution:
First, determine the time to reach the maximum height (when velocity becomes 0 m/s).
Then, calculate the time it takes for the ball to descend from the maximum height to the branch.
Subtract the time it took to reach the branch on the way up from the total time to determine the additional time.
By following these steps, we can find that the additional time the ball will take to pass the tree branch on its way back down is the time from the peak of its trajectory to the 7.00 m height minus the time it took to initially reach 7.00 m on the way up.