Question

M A 45.0 -kg girl is standing on a 150 -kg plank. 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 of 1.50 i^ m/s relative to the plank. (a) What is the velocity of the plank relative to the ice surface?

Answer 1

The plank's velocity relative to the ice surface is 0.45 m/s in the opposite direction of the girl's motion, ensuring conservation of momentum.

Step-by-step explanation:

The student's question involves a concept in physics related to conservation of momentum. Since the system is isolated and there are no external forces, the total momentum of the system before and after the girl starts walking must be the same. As the girl and the plank are initially at rest, their collective momentum is zero. When the girl starts walking at a velocity of 1.50 m/s relative to the plank, the plank must move in the opposite direction to conserve momentum.

The girl's momentum is given by the product of her mass and velocity, which is 45.0 kg × 1.50 m/s = 67.5 kg·m/s. The plank's velocity can be calculated using the formula:
plank's velocity = - (girl's momentum / plank's mass) = - (67.5 kg·m/s) / 150 kg = -0.45 m/s.

Therefore, the velocity of the plank relative to the ice will be 0.45 m/s in the direction opposite to the girl's motion.

Answer 2

The velocity of the plank relative to the ice surface is 1.50 i^ m/s.

Step-by-step explanation:

To find the velocity of the plank relative to the ice surface, we need to consider the conservation of momentum. The total momentum of the system before the girl starts walking is zero since both the girl and the plank are at rest. After the girl starts walking, the total momentum of the system remains zero according to the law of conservation of momentum. Since the girl and the plank are a part of the same system, their momenta should cancel each other out. Therefore, the velocity of the plank relative to the ice surface would also be 1.50 i^ m/s.