A `2kg` block slides on a horizontal floor with the a speed of `4m//s` it strikes a uncompressed spring , and compresses it till the block is motionless . The kinetic friction force is compresses is `15 N` and spring constant is `10000 N//m` . The spring by

Options

A. 5.5 cm
B. 2.5 cm
C. 11.0 cm
D. 8.5 cm

Answer

C

Explanation

`(1)/(2)mv^2=(1)/(2)kx^2+W_f`
`(1)/(2)(2)(4)^2=(1)/(2)(10000)x^2+f_(k)x`
`16=5xx10^3x^3+15x`
`5xx10^3x^3+15x-16=0`
`x=(-15+-sqrt((15)^2+4xx5xx10^2xx16))/(5xx10^3)`
`=(11)/(100)m=11cm`