Question

A 50.0-kg student stands on a 150-kg wooden plank. Both start at rest on a frozen pond (assume the interface between pond and plank is frictionless). The student then walks with a constant velocity of 1.10 im/s relative to the plank. (a) What is the velocity of the plank relative to the frozen pond?

Answer 1

0.275 m/s in the opposite direction

Step-by-step explanation:

m = Mass of student = 50 kg

M = Mass of plank = 150 kg

`v_r` = Velocity of the student with respect to the plank = 1.1i m/s

As the linear momentum is conserved in the system

`m(v_r+v)+Mv=0\\\Rightarrow v(m+M)=-mv_r\\\Rightarrow v=-(mv_r)/(m+M)\\\Rightarrow v=-(50* 1.1i)/(50+150)\\\Rightarrow v=-0.275i\ m/s`

The plank will move at 0.275 m/s in the opposite direction