Vertical motion of a bouncing ball

In this experiment, you will measure the motion of a ball after it bounces off the floor.

Fix a meterstick so it stands vertically against the edge of a table.
Drop a ball from the stop of the meterstick, at a height H = 100 cm above the floor.
Wait for the ball to strike the floor and bounce back up. As it does ...
- measure the time from its first bounce to the second bounce, when it returns to the floor. Call this time T.
- measure the maximum height to which the ball bounces. Call this height h. (Yes, it is difficult to do this accurately. Don't worry, just do what you can.)

Repeat step "c" five (5) times, so that you have five values of T and h.

Now, for the analysis.

Compute the mean and standard deviation of the values of T.
Using only these values of time, calculate the initial upwards velocity v_i of the ball after its first bounce. Compute the uncertainty in this velocity, too. Write them both down clearly.

Compute the mean and standard deviation of the values of h.
Using only these values of height, calculate the initial upwards velocity v_i of the ball after its first bounce. Compute the uncertainty in this velocity, too. Write them both down clearly.