A 48.2 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 2.00 m/s to the right relative to the plank.
(a) What is her velocity relative to the surface of the ice?
To find the girl's velocity relative to the surface of the ice, we need to consider the conservation of momentum.
The initial momentum of the system (girl + plank) is zero, as both are at rest. The final momentum of the system will also be zero, as there are no external forces or friction acting on the system.
The momentum equation can be written as:
initial momentum = final momentum
Initially, the girl has no velocity, so her momentum is zero (m1 * v1 = 0).
The plank has no velocity, so its momentum is also zero (m2 * v2 = 0).
At the final state, the girl and the plank move together with a constant velocity of 2.00 m/s to the right relative to the plank. Let's denote this velocity as vf.
The girl's mass is m1 = 48.2 kg, and the plank's mass is m2 = 160 kg.
Using the equation for momentum:
m1 * v1 + m2 * v2 = 0
Substituting the given values:
48.2 kg * 0 + 160 kg * vf = 0
vf = 0
Therefore, the girl's velocity relative to the surface of the ice is zero.