Final answer:
A ball thrown vertically upward is caught by the thrower after 2.60 seconds; this statement is true due to the symmetry in the ball's parabolic trajectory under the constant acceleration of gravity.
Step-by-step explanation:
True. When a ball is thrown vertically upward, it follows a parabolic trajectory due to the acceleration of gravity. Assuming acceleration due to gravity is approximately -9.81 m/s2 (negative as it's directed downwards), the ball will decelerate as it rises, eventually reaching a momentary stop at the highest point of its trajectory. It will then begin to accelerate downwards until it's caught by the thrower.
The total time taken for this two-part journey (upward and then downward) can be determined by doubling the time it takes for the ball to reach its highest point. Given that it takes 2.60 seconds for the entire trip, the ball would have taken 1.30 seconds to reach the peak of its trajectory. This symmetry is due to the constant acceleration caused by gravity. Therefore, the statement that a ball thrown vertically upward is caught by the thrower after 2.60 seconds is true.