Two people, George who has a mass of 86.0 kg and Victoria who has a mass of 57.0 kg, are on a frozen circular pond. They stand at the very centre and push off of each other. The distance from one side of the pond to the other is 86.0 m and it takes George 14.0 s to reach the edge of the pond. How long does it take Victoria to reach the edge of the pond?
Question
Two people, George who has a mass of 86.0 kg and Victoria who has a mass of 57.0 kg, are on a frozen circular pond. They stand at the very centre and push off of each other. The distance from one side of the pond to the other is 86.0 m and it takes George 14.0 s to reach the edge of the pond. How long does it take Victoria to reach the edge of the pond?
Solution
To solve this problem, we need to use the principle of conservation of momentum. The total momentum before they push off each other is zero (because they are initially at rest), and the total momentum after they push off each other is also zero (because there are no external forces).
The momentum of each person is given by the product of their mass and velocity. Let's denote the velocity of George as Vg and the velocity of Victoria as Vv.
From the conservation of momentum, we have:
86.0 kg * Vg = 57.0 kg * Vv
We can solve this equation for Vv:
Vv = (86.0 kg / 57.0 kg) * Vg
We know that the distance George travels is half the diameter of the pond, or 43.0 m. The time it takes him to travel this distance is 14.0 s. Therefore, his velocity is:
Vg = 43.0 m / 14.0 s = 3.071 m/s
Substituting this into the equation for Vv, we get:
Vv = (86.0 kg / 57.0 kg) * 3.071 m/s = 4.63 m/s
The distance Victoria needs to travel is also 43.0 m. Therefore, the time it takes her to reach the edge of the pond is:
t = 43.0 m / 4.63 m/s = 9.29 s
So, it takes Victoria approximately 9.29 seconds to reach the edge of the pond.
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