College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

This is a symbolic version of Problem 23. 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.) (a) What is the velocity vPI of the plank relative to the surface of the ice? (b) What is the girl’s velocity vGI relative to the ice surface?

(a)

To determine
Velocity of the Plank relative to the Ice.

Explanation

Given Info The velocity of the girl relative to the ice is,

vâ†’GI=vâ†’GP+vâ†’PI (1)

• vâ†’GI is the velocity of the girl relative to the ice.
• vâ†’GP is the velocity of the girl relative to the Plank.
• vâ†’PI is the velocity of the Plank relative to the ice.

Apply conservation of momentum to girl â€“ plank system,

(mGvâ†’GI+mPvâ†’PI)i=(mGvâ†’GI+mPvâ†’PI)f (2)

Rewrite the above equation with zero as the initial velocity of the girl and plank,

(mGvâ†’GI+mPvâ†’PI)f=0 (3)

Solve equation (2) for vPI by substituting the equation (1)

(b)

To determine
Velocity of the girl relative to the ice

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