Hot air balloon flying is a popular recreation in several southwestern states. At some gatherings of balloonists, there is a competition to hit targets on the group with bags dropped from balloons at various altitudes. The balloons drift toward and over the target at various speeds. To have the best chance that their drop bags will hit the target, balloonists need to know how fast the bags will fall toward the ground. Principles of physics predict that the velocity in feet per second will be a function of time in seconds with the rule V equals 32 t. The distance fallen in feet will also be a function of time in seconds with rule D equals 16 t squared.

a. How long will it take the drop bag to reach velocity of:
48 feet per second?
100 feet per second?
150 feet per second?

b. What rule can be used to calculate values for the inverse of the velocity function—to find the time when any given velocity will be reached?

c. How long will it take the drop bag to reach the ground from altitudes of:
144 feet?
400 feet?
500 feet?

d. What rule can be used to calculate values of the inverse of the distance function—to find the time it takes for the drop bag to fall any given distance?

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