Answer:
Part A:
(a): -121.26 ft/s.
(b): -121.13 ft/s.
(c): -121.052 ft/s.
(d): -121.026 ft/s.
Part B:
-121.00 ft/s.
Step-by-step explanation:
Given that the height of the balloon after t seconds is

The average velocity of an object is defined as the total distance traveled by the object divided by the time taken in covering that distance.

where,
are the positions of the object at time
and
respectively.
Part A:
- For the average velocity for the time period beginning when t=3 and lasting .01 sec.
For this case,
- For the average velocity for the time period beginning when t=3 and lasting .005 sec.
For this case,

- For the average velocity for the time period beginning when t=3 and lasting .002 sec.
For this case,

- For the average velocity for the time period beginning when t=3 and lasting .001 sec.
For this case,

Part B:
The instantaneous velocity of the balloon at the given time is defined as the rate of change of its position at that time.

Note: The negative sign with all the velocities indicates that the direction of these velocities are downwards.