Part 1
A 36 kg girl is standing on a 65 kg plank. The
plank, originally at rest, is free to slide on a
frozen lake, which is a flat, frictionless supporting surface. The girl begins to walk along the plank at a constant speed of 1.89 m/s to
the right relative to the plank.
What is her velocity relative to the ice surface?
Answer in units of m/s
Part 2
the plank at a constant speed of 1.89 m/s to
the right relative to the plank.
What is her velocity relative to the ice surface?
Answer in units of m/s
Part 1: To find the girl's velocity relative to the ice surface, we need to consider the concept of relative motion.
When the girl walks on the plank, she's essentially adding her velocity to the velocity of the plank. Since the girl is moving to the right relative to the plank, her velocity relative to the ice surface will be the sum of her velocity relative to the plank and the velocity of the plank.
Given that the girl's velocity relative to the plank is 1.89 m/s to the right, we need to determine the velocity of the plank.
To find the velocity of the plank, we can use the principle of conservation of momentum. In this case, since there are no external forces, the total momentum of the system (girl + plank) will be conserved.
The initial momentum of the system is zero since both the girl and the plank are at rest. After the girl starts walking, her momentum will be m₁ * v₁, where m₁ is her mass and v₁ is her velocity relative to the plank. The momentum of the plank will be m₂ * v₂, where m₂ is the mass of the plank and v₂ is its velocity.
Since momentum is conserved, we can equate the initial and final momentum:
0 = m₁ * v₁ + m₂ * v₂
Rearranging the equation, we get:
v₂ = -(m₁ / m₂) * v₁
Substituting the given values, with m₁ = 36 kg (mass of the girl) and m₂ = 65 kg (mass of the plank), and v₁ = 1.89 m/s (girl's velocity relative to the plank), we can calculate v₂:
v₂ = -(36 kg / 65 kg) * 1.89 m/s
Simplifying the expression, we get:
v₂ ≈ -1.046 m/s
So, the velocity of the plank is approximately -1.046 m/s to the left.
Now, to find the girl's velocity relative to the ice surface, we add her velocity relative to the plank to the velocity of the plank:
Velocity of girl relative to ice surface = velocity of girl relative to the plank + velocity of the plank
Velocity of girl relative to ice surface = 1.89 m/s (to the right) + (-1.046 m/s) (to the left)
Velocity of girl relative to ice surface ≈ 0.844 m/s to the right
Therefore, the girl's velocity relative to the ice surface is approximately 0.844 m/s to the right.
Part 2: In this part, it seems like there is a repetition of Part 1. The answer would remain the same as in Part 1, which is approximately 0.844 m/s to the right.