In a free fall, the body passed 5 m in the first second, and 10 m more in each next. Find the depth of the mine if the freely falling body reaches its bottom 5 seconds after the start of the fall.
1. Let’s solve this problem using an arithmetic progression.
a1 = 5;
d = 10;
2. It is required to find the sum of the first five members. Let’s write down the formulas for the sum:
Sn = (2a1 + (n – 1) * d) / 2 * n;
Sn = (a1 + an) / 2 * n;
We use the first formula, since the first term and d are known.
3. Find the sum:
S5 = (2 * 5 + (5 – 1) * 10) / 2 * 5 = 125;
That is, the body has traveled 125 meters.
Answer: the depth of the mine is 125 meters.
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