Abby throws a ball straight up and times it. she sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.10 s. what was the speed of the ball at as it passed the top of the flagpole?

The time it takes for a ball to complete the trip is given to be 4.10 s. This implies that the trip going up of the ball is equal to 2.05 s. Using this time to determine the initial speed, we have,
                                   Vf = Vo - gt
Vf is the final speed which is equal to 0 on the topmost location of the ball.
                                     0 = Vo - (9.8 m/s²)(2.05 s)
                                        Vo = 20.09 m/s

At 0.5 s,
                                    Vf = 20.09 m/s - (9.8 m/s²)(0.5 s)
                                          Vf = 15.19 m/s

Thus, the speed of the ball when the height is in level with the top of the flagpole is 15.19 m/s.