A shot travelling at the rate of `100ms^(-1)` is just able to pierce a plank 4cm thick. What velocity is required to jut pierce a plank 9cm thick?

Explanation

`v_(1)=100m//s`
`s_(1)=4cm`
`s_(2)=9cm`
`v_(2)=??`
Formula:
K.E lost = Work done against plank's resistance.
`(1)/(2)mv_(1)^(2)=Fxxs_(1)" "....(1)`
`(1)/(2)mv_(2)^(2)=Fxxs_(2)" "....(2)`
`((2))/((1))implies(v_(2)^(2))/(v_(1)^(2))=(s_(2))/(s_(1))implies(v_(2))/(v_(1))=sqrt((s_(2))/(s_(1)))`
`(v_(2))/(v_(1))=sqrt((9)/(4))=(3)/(2)impliesv_(2)=(3)/(2)xxv_(1)`
`v_(2)=(3)/(2)xx100=150m//s`