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A 45.0-kg girl is standing on a 160-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.44 m/s to the right relative to the plank. (Let the direction the girl is moving in be positive. Indicate the direction with the sign of your answer.)
(a) What is her velocity relative to the surface of ice?
m/s
(b) What is the velocity of the plank relative to the surface of ice?
m/s
a) 0=45*(1.44+V)+160V
V=-0.316m/s
1.44+V=1.44-0.316=1.124m/s
To find the answers to these questions, we need to apply the principle of conservation of momentum.
(a) The velocity of the girl relative to the surface of the ice can be found by summing up the individual velocities of the girl and the plank. Since the girl is moving to the right, we assign a positive sign to her velocity. The velocity of the plank is zero since it is at rest. The equation for the conservation of momentum is:
(mass of girl * velocity of girl) + (mass of plank * velocity of plank) = 0
Substituting the given values:
(45 kg * velocity of girl) + (160 kg * 0) = 0
45 kg * velocity of girl = 0
velocity of girl = 0 / 45 kg
velocity of girl = 0 m/s
Therefore, her velocity relative to the surface of ice is 0 m/s.
(b) The velocity of the plank relative to the surface of ice can be found by subtracting the velocity of the girl from the sum of the velocities of the girl and the plank. The equation is:
(velocity of girl + velocity of plank) = velocity of plank relative to the surface of ice
Substituting the given values:
(1.44 m/s + velocity of plank) = velocity of plank relative to the surface of ice
Since the surface of ice is frictionless, there is no external force acting on the system. Therefore, the net force is zero, and the acceleration is also zero. As a result, the velocity of the plank will remain constant.
Hence,
1.44 m/s + velocity of plank = velocity of plank relative to the surface of ice
velocity of plank relative to the surface of ice = 1.44 m/s
Therefore, the velocity of the plank relative to the surface of ice is 1.44 m/s to the right.