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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?

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Answer:

0.275 m/s in the opposite direction

Explanation:

m = Mass of student = 50 kg

M = Mass of plank = 150 kg

[tex]v_r[/tex] = Velocity of the student with respect to the plank = 1.1i m/s

As the linear momentum is conserved in the system

[tex]m(v_r+v)+Mv=0\\\Rightarrow v(m+M)=-mv_r\\\Rightarrow v=-\frac{mv_r}{m+M}\\\Rightarrow v=-\frac{50\times 1.1i}{50+150}\\\Rightarrow v=-0.275i\ m/s[/tex]

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

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