A `45.0kg` girl is standing on plank that has a mass of `150kg`. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless supporting surface. The girl begins to walk alnong the plank at a constant speed of `1.50m//s` relative to the plank. (a) What is her speed relative to the ice surface? (b) What is the speed of the plank relative to the ice surface?

Answer

15/13m/s (b) `-9//26m//s`

Explanation

`m_("girl")v_("girl")+m_("plank")v_("plank")=0` [Initially both at reat]
`rArr" "45v_("girl")+150v_("plank")=0`…(i)
`v_("girl/plank")=v_("girl")-v_("plank")=1.5`…(ii)
Solving(i)and(ii),we get
`v_("girl")=(1.5xx150)/(195)=(15)/(13)m//s`
`v_("plank")=v_("girl")-1.5=(15)/(13)-(3)/(2)`
`v_("plank")=-(9)/(26)m//s`