Question

A girl of mass mg is standing on a plank of mass mp. Both are 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 vgp to the right relative to the plank. (The subscript gp denotes the girl relative to plank. Use any variable or symbol stated above as necessary.)

1.) What is the velocity vpi of the plank relative to the surface of the ice?


2.) What is the girl's velocity vgi relative to the ice surface?

Any help understanding this would be appreciated. Thanks.

Answer 1

Answer:

Part a)

$v_{pi} = \frac{m_g v_{gp}}{m_g + m_p}$

Part b)

$v_{gi} =  \frac{m_p v_{gp}}{m_g + m_p}$

Explanation:

As we know that there is no external force on the system of girl and plank

so we will say that total momentum of girl and plank will remains conserved

so we will say

$m_g v_{gi} + m_pv_{pi} = 0$

now here we know that girl move with respect to plank with speed $v_{gp}$

now let say that the plank moves with speed v opposite to the motion of girl

so we have

$m_g(v_{gp} - v_{pi}) + m_p(-v_{pi}) = 0$

$m_gv_{gp} = (m_g + m_p) v_{pi}$

$v_{pi} = \frac{m_g v_{gp}}{m_g + m_p}$

Part b)

also the speed of girl with respect to the ice surface is given as

$v_{gi} = v_{gp} - v_{pi}$

$v_{gi} = v_{gp} -  \frac{m_g v_{gp}}{m_g + m_p}$

$v_{gi} =  \frac{m_p v_{gp}}{m_g + m_p}$