Question

Please help
Medal
A rifle loses 1/n of its velocity in passing through a plank .what is the least no. Of plank required to stop the bullet

Answer 1

taking your question at face value, velocity goes like this after each plank \(v = v_0 \to v = v_o {n-1 \over n} \to v = v_o ({n-1 \over n})^2 \to v = v_o({n-1 \over n})^3 \to \dots \), ie there is no point at which v = 0, it is asymptotic but never gets to zero

what you might actually have in mind is that \(v = v_0 \to v = v_o - {v_o \over n} \to v = v_o - {v_o \over n} - {v_o \over n} \to v = v_o - {v_o \over n} - {v_o \over n} - {v_o \over n} \to \dots\)

which is a much simpler idea as this is \(v = v_0 \to v = v_o - v_o{1 \over n} \to v = v_o - v_o{2 \over n} \to v = v_o - v_o{3 \over n} \to \dots\)

you might wish to link / scan the actual question :p