Question

A bullet traveling horizontally losses 1/20th of its velocity while penetrating a wooden plank, how many sucj planks are required to stop the bullet?

Answer 1

Step-by-step explanation:

if it is just defined as geometric sequence

an = an-1 × 0.8

then infinitely many. that way we will never reach 0 velocity. the sequence will go on in all eternity with the next velocity being 80% of the previous velocity. and 80% of that. and so on.

it will get closer and closer to 0 but never reach it.

under normal (natural, physical) circumstances we need a stop criteria, like the minimum velocity for a bullet to penetrate such a plank.

once we have that, we can calculate (initial velocity × 0.8^n < minimum velocity) after how many planks (n) the bullet reaches that velocity. and that gives us the number.