A 43.3 kg girl is standing on a 125 kg plank.
The plank, originally at rest, is free to slide on
a frozen lake, which is a flat, frictionless sup-
porting surface. The girl begins to walk along
the plank at a constant speed of 1.87 m/s to
the right relative to the plank.
What is her velocity relative to the ice sur-
face?
Answer in units of m/s
What is the velocity of the plank relative to
the ice surface?
Answer in units of m/s
To find the velocity of the girl relative to the ice surface, we need to consider the relative motion between the girl and the ice surface.
Given:
Mass of the girl (m1) = 43.3 kg
Mass of the plank (m2) = 125 kg
Speed of the girl relative to the plank (v1) = 1.87 m/s (to the right)
We can use the principle of conservation of momentum to find the velocity of the girl relative to the ice surface. The total momentum before the girl starts walking is zero (as the system is initially at rest). The total momentum after the girl starts walking will also be zero because there are no external forces acting on the system.
Let's assume:
Velocity of the girl relative to the ice surface (V) = v2
Velocity of the plank relative to the ice surface (U) = v3
Now let's apply the principle of conservation of momentum:
Initial momentum = Final momentum
(0 kg) + (0 kg) = (mass of girl) × (velocity of the girl relative to the ice surface) + (mass of plank) × (velocity of the plank relative to the ice surface)
0 = (43.3 kg) × v2 + (125 kg) × v3
Since the girl and the plank move together as a system, their velocities are equal in magnitude but opposite in direction. So, we have:
v2 = -v3
By substituting this into the momentum equation, we get:
0 = (43.3 kg) × v2 - (125 kg) × v2
Simplifying this equation, we find:
v2 = 0 m/s
Therefore, the velocity of the girl relative to the ice surface is 0 m/s.
To find the velocity of the plank relative to the ice surface, we can use the fact that v3 = -v2. From the above calculation, we know that v2 = 0 m/s. Substituting this into the equation, we get:
v3 = -0 m/s
Therefore, the velocity of the plank relative to the ice surface is also 0 m/s.