A block of mass 200 g is given velocity `2(m)//(s)` on a horizontal surface as shown in the figure. Find the maximum compression of spring of spring constant `k=100(N)//(m)`

Explanation

Between (1) and (2)
`(1)/(2)mv_0^2=(1)/(2)kx_0^2+W_f`
`=(1)/(2)kx_0^2+mumgx_0`
`v_0^2=(k)/(m)x_0^2+2mugx_0`
`(2)^2=(100)/(0.2)x_0^2+2xx0.5xx10x_0`
`100x_0^2+2x_0-0.8=0`
`x_0=(-2+-sqrt((2)^2-4(100)(-0.8)))/(200)`
`=(-2+-sqrt(4+320))/(200)=(-2+-18)/(200)`
`=(16)/(200)=(8)/(100)=8cm`