Two people wearing skates facing each other. The 1st person is 75kg and pushes the second person 60 kg away at a speed of 2.0 m/s. What is the speed of the 1st person?
To find the speed of the 1st person after pushing the second person away, we can make use of the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum before the push is equal to the total momentum after the push.
The momentum of an object is defined as the product of its mass and velocity (p = m * v).
Let's assume the initial velocity of the 1st person is u1 and the initial velocity of the 2nd person is u2. After the push, the velocities change to v1 and v2, respectively.
The total momentum before the push can be calculated as follows:
Initial momentum = (mass of the 1st person * initial velocity of the 1st person) + (mass of the 2nd person * initial velocity of the 2nd person)
Initial momentum = (75 kg * u1) + (60 kg * u2)
The total momentum after the push can be calculated as follows:
Final momentum = (mass of the 1st person * final velocity of the 1st person) + (mass of the 2nd person * final velocity of the 2nd person)
Final momentum = (75 kg * v1) + (60 kg * v2)
According to the principle of conservation of momentum, the initial momentum and the final momentum are equal: Initial momentum = Final momentum.
So we have the equation: (75 kg * u1) + (60 kg * u2) = (75 kg * v1) + (60 kg * v2)
Now let's plug in the given values in the equation. We know the mass of the 1st person is 75 kg, the mass of the 2nd person is 60 kg, and the initial velocity of the 2nd person is 0 m/s (since they are initially at rest).
The equation becomes: (75 kg * u1) = (75 kg * v1) + (60 kg * 0 m/s)
Simplifying: (75 kg * u1) = (75 kg * v1)
Dividing both sides by 75 kg, we get: u1 = v1
Therefore, the speed of the 1st person after pushing the second person away is the same as their initial speed, which is 2.0 m/s.