A ball falls freely from rest at a height of 2 meters. Observations indicate that the ball reaches the ground in .64 seconds.

Based on this information what is its acceleration?

so you must first start out with the displacement equation so you can find vf ... 2m=((vf-0m/s)/2)*.64s

manipulate w/ algrebra to give you (4m/.64s)-0m/s=vf

vf=6.25m/s

now use the a=(6.25m/s)/(.64s)=9.8m/s/s

Is this consistent with an observation which concludes that a ball dropped from a height of 5 meters reaches the ground in 1.05 seconds?

starting out with the same scenario you must find vf to do so you must manipulate the equation for displacement... 5m=((Vf-0m/s)/2)*1.05s

now vf=(10m/1.05s)-0m/s=9.524m/s

now a=(9.524m/s)/1.05s

a=9.07m/s/s so yes its pretty close

Are these observations consistent with the accepted value of the acceleration of gravity, which is 9.8 m / s^2?

yes the observation seem pretty close so it would seem that 9.8m/s/s is a reasonable estimate of gravity

10-15min