Here we're applying a basic physics rule for vertical motion where the only pull on the object is gravity.
This rule has the form
h(t) = h + v t + (1/2)a*t^2
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To adapt this rule to this particular question replace h with 0, as the
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upward path of the object begins at 0 ft. Replace v with +15 ft/sec.
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Replace "a" with (-32.2 ft/(sec^2); this is the acceleration due to gravity.
Then we have the following, with the label F(t):
F(t) = 0 + (15 ft/sec)t + (1/2)(-32.2 ft)/(sec^2), or
F(t) = 15t - 16.1t^2. Thus, Choice D is correct.
Please note: To avoid confusion, please use " ^ " to denote exponentiation:
F(t) = -16t^2 + 15t
