A father (mF = 83 kg) and his daughter (mD= 43 kg) stand on a flat frozen lake of negligible friction. They hold a 13 m long rope stretched between them. The father and daughter then pull the rope to bring them together. If the father is initially standing at the origin, how far from the origin will they meet?
What equation would I use to determine this?
conservation of momentum, first collary.
the center of gravity does not change if it was still before.
CG= (0*83+13*43 )/(83+43)
and it does not move. That is where they will meet.
To determine the distance from the origin where the father and daughter will meet, you can use the concept of center of mass. The equation that you can use in this case is the weighted average equation for the position of the center of mass:
x_cm = (mF * xF + mD * xD) / (mF + mD)
In this equation:
- x_cm is the position of the center of mass.
- mF and mD are the masses of the father and daughter, respectively.
- xF and xD are the initial positions of the father and daughter, respectively.
In this scenario, since the father is initially standing at the origin, his initial position (xF) is 0. The daughter's initial position (xD) is given by the length of the rope, which is 13 m.
Plugging in these values into the equation, the equation becomes:
x_cm = (83 kg * 0 + 43 kg * 13 m) / (83 kg + 43 kg)
Simplifying this equation, you can calculate the position of the center of mass, which will give you the distance from the origin where the father and daughter will meet.