Final answer:
The mass of the ball that reaches a height of 15 ft cannot be determined from the height alone since the height a ball reaches when tossed is independent of its mass under the conditions described. The problem given is related to calculating the time taken for a ball thrown vertically to pass a specific height during its ascent and descent.
Step-by-step explanation:
The mass of the ball is irrelevant when considering how high it is tossed, as long as we are ignoring air resistance and assuming Earth's gravity is the only force acting on it after the ball is released. The question regarding the mass m of the ball that reaches a height of 15 ft cannot be answered with the information provided because the height achieved by the ball does not depend on its mass. For the problem shared which includes the initial velocity and the passing height by the tree branch, we can calculate the additional time it will pass before the ball descends past the tree branch again based on kinematic equations.
We would use the kinematic equation for the ball's vertical motion to find the time to reach the maximum height and then use symmetry of the motion to determine the total time for ascent and descent back to the tree branch height.