Suppose you are galileo measure the acceleration due to gravity by dropping a canon ball from the tower of pisa, you measure the height of the tower to be h =183 ft, and you estimate that the uncertainty is delta h=0.2 ft. you measure the drop time using your pulse and arrive at delta t =3.5 sec with an estimated uncertainty delta t= 0.5 sec. you perform the experiment just one time. if the formula propagated error is delta g= g (√(delta h/h)^2 +(2* delta t/t)^2) what would you report as your result (including uncertainty) in ft/sec?

It is given that the height of the tower is

The uncertainty the measurement of this height is

Drop time is measured as:

The uncertainty in measurement of time is:

Using the equation of motion: where, is the distance covered, is the initial velocity, is the acceleration and is the time.

(because canon ball is in free fall). we need to calculate the value of a=g.

The uncertainty in this value is given by:

Substitute the values:

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.