Answer
$464\ ft$, $3600\ ft$
Work Step by Step
Step 1. Based on the given conditions, we have
$a_1=16, a_2=48, a_3=80, a_4=113$
We can identify this as an arithmetic series with $d=32$. Thus
$a_n=a_1+(n-1)d=16+32(n-1)=32n-16\ ft$
Step 2. For $n=15$, we have
$a_{15}=32(15)-16=464\ ft$
(fall distance during the 15th second)
Step 3. The sum of the first 15 terms is
$S_{15}=\sum_1^{15}a_i=\frac{15}{2}(a_1+a_{15})=\frac{15}{2}(16+464)=3600\ ft$
(total fall distance in 15 seconds)
