Two students on roller skates stand face-to-face, then push each other away. One student has a mass of 94 kg, the other 65 kg. Find the ratio of the velocities just after the hands lose contact.

To find the ratio of the velocities just after the hands lose contact, we can use the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. In this scenario, the students are only exerting forces on each other, so the total momentum of the system before and after the push will be the same.

The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is equal to mass (m) multiplied by velocity (v): p = m * v.

Let's represent the mass of the first student as m1 (94 kg) and the mass of the second student as m2 (65 kg), and let's represent their velocities just after the hands lose contact as v1 and v2, respectively.

According to the conservation of momentum, the total initial momentum (before the push) should be equal to the total final momentum (after the push).

The initial momentum of the system will be the sum of the momentum of each student. Therefore, the initial momentum (before the push) can be calculated as:
initial momentum = m1 * v1 + m2 * v2

Similarly, the final momentum (after the push) can be calculated as:
final momentum = m1 * v1' + m2 * v2'

Since the total momentum is conserved, we can equate the initial and final momentum equations:
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'

Now, let's determine the ratio of the velocities just after the hands lose contact. Dividing both sides of the equation by m1 * m2, we get:
(v1 + v2) / (v1' + v2') = 1

Therefore, the ratio of the velocities just after the hands lose contact is 1.

1:1