Question

A 44.8-kg girl is standing on a 159-kg plank. Both originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.48î m/s relative to the plank.

(a) What is the velocity of the plank relative to the ice surface?

(b) What is the girl's velocity relative to the ice surface? î m/s

Answer 1

Figure shows the movement of girl, movement of plank and stationary position of centre of mass.

Initially let us assume, girl stands at centre of plank C so that the centre of mass of the combined system coincides with centre of plank. If the girl moving towards left for a distance x_g from centre of plank C ,

then x-coordinate of centre of mass CM_X with respect to plank is given by,

CM_X = ( m_g x_g ) / ( m_g + m_p ) .........................(1)

Hence the distance moved by plank with respect to ice towards -ve x-direction is -CM_X = -( m_g x_g ) / ( m_g + m_p )

(1) velocity of the plank with respect to ice :- - v_g( m_g ) / ( m_g + m_p ) = -1.48 ( 44.8)/(44.8+159) = -.325 m/s

(2) Girls velocity with respect to ice :- (v_g - v_p) = ( 1.48 - 0.325 ) m/s = 1.154 m/s