Question 287344
Use a(t) = -32 ft/sec^2 as the acceleration due to gravity. (Neglect air resistance.) 
A balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 48 feet above the ground.
The height of the bag as a function of time in seconds is:
h(t) = -16t^2 + 16t + 48
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a) How many seconds after its release will the bag strike the ground?
Find t when h(t) = 0
-16t^2 + 16t + 48 = 0
-t^2 + t + 3 = 0
(-t - 1)*(t -3) = 0
t = 3 seconds
Ignore the t = -1 second
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b) At what velocity will it strike the ground? 
vertical speed after release = 16 - 32t
= 16 - 96
= -80 ft/sec  (negative is the down direction)