Question Number 192257 by Tomal last updated on 13/May/23
$$ \\ $$$$\mathrm{A}\:\mathrm{bullet}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{30}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{after} \\ $$$$\mathrm{pentrating}\:\mathrm{a}\:\mathrm{6}\:{cm}\:\mathrm{whole}\:\mathrm{tree}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{is}\: \\ $$$$\mathrm{reduced}\:\mathrm{by}\:\mathrm{one}−\mathrm{third}\:\mathrm{and}\:\mathrm{then}\:\mathrm{the}\:\mathrm{bullet} \\ $$$$\mathrm{travel}{s}\:\mathrm{for}\:\mathrm{1s}\:\mathrm{more}.\: \\ $$$$ \\ $$$$ \\ $$$${Will}\:\mathrm{the}\:\mathrm{bullet}\:\mathrm{penetratee} \\ $$$$\mathrm{th}\:\mathrm{tree}?\:\mathrm{Analyze}\:\mathrm{mathematically}. \\ $$
Commented by AST last updated on 13/May/23
$${Maybe}\:{it}\:{should}\:{be}\:“…{after}\:{hitting}\:{a}\:\mathrm{6}{cm}…'' \\ $$
Commented by Tinku Tara last updated on 13/May/23
$$\mathrm{question}\:\mathrm{is}\:\mathrm{not}\:\mathrm{clear}.\:\mathrm{probably}\:\mathrm{issue} \\ $$$$\mathrm{with}\:\mathrm{translation} \\ $$
Commented by AST last updated on 16/Oct/23
$${The}\:{velocity}\:{of}\:{the}\:{bullet}\:{reduces}\:{to}\:\mathrm{20}{ms}^{−\mathrm{1}} \\ $$$${after}\:{hitting}.\:{This}\:{implies}\:{it}\:{travels}\:{a}\:{distance} \\ $$$${of}\:\mathrm{20}{m}\:{after}\:\mathrm{1}{s}\left({assuming}\:{the}\:{speed}\:{was}\:\right. \\ $$$$\left.{constant}\right)..\:{Suppose}\:{the}\:{bullet}\:{stopped}\:{after}\:\mathrm{1}{s} \\ $$$${v}={u}+{at}\Rightarrow\mathrm{0}=\mathrm{20}+{a}\Rightarrow{a}=−\mathrm{20}{ms}^{−\mathrm{2}} \\ $$$${s}={ut}+\frac{{at}^{\mathrm{2}} }{\mathrm{2}}=\mathrm{20}−\mathrm{10}=\mathrm{10}{m}.\: \\ $$$${Since}\:\mathrm{20}{m}>\mathrm{10}{m}>\mathrm{6}{cm},\:{the}\:{bullet}\:{penetrates}\: \\ $$$${the}\:{tree}\:{in}\:{both}\:{cases}. \\ $$