Final answer:
A ball thrown vertically upwards takes the same amount of time to fall back down as it took to rise and come to a stop. Therefore, if it takes 9 seconds to stop, it will also take 9 seconds to fall back down.
Step-by-step explanation:
Based on the principles of physics and the properties of free fall, when a ball is thrown vertically with an upward force, it will decelerate due to gravity until it comes to a stop, which in this case takes 9 seconds. This period of ascent is equal to the period of descent, because gravity is a uniform force and it acts on the ball both while it is moving upward and downward. Thus, if the ball takes 9 seconds to slow down and stop at its highest point, it will take an additional 9 seconds to fall back down to its original launch position. Considering air resistance is negligible, the symmetrical nature of the motion ensures that the ascent and descent times are equal. Therefore, the ball would also take 9 seconds to fall back down after it has come to a stop at its peak.
The amount of time an object is in free fall will depend on its velocity and the distance it falls. Similar to distance, there are two equations you can use to find the time, depending on what you know.
Formula for Finding Time Using Velocities
vf=vi+atvf=vi+at