Question

In pairs figure-skating competition, a 65-kg man and his 45-kg female partner stand facing each other both at rest on the ice. If they push apart and the woman has a velocity of 1.5 m/s eastward, what is the velocity of her partner? (Neglect friction.)

Answer 1

When the female partner pushes off with a velocity of 1.5 m/s eastward, the velocity of her male partner is -1.04 m/s westward.

Step-by-step explanation:

In this situation, we can use the law of conservation of momentum to find the velocity of the male partner. The law states that the total momentum before a collision is equal to the total momentum after the collision, as long as no external forces are acting on the system.

Initially, the total momentum of the system is 0 kg*m/s since both the man and woman are at rest. When the woman pushes off with a velocity of 1.5 m/s eastward, her momentum is given by:

Momentum of the woman = mass of the woman * velocity of the woman

Momentum of the woman = 45 kg * 1.5 m/s = 67.5 kg*m/s

According to the law of conservation of momentum, the total momentum after the push must also be 0 kg*m/s. Therefore, the momentum of the man must be:

Momentum of the man = -Momentum of the woman

Momentum of the man = -67.5 kg*m/s

Since the mass of the man is 65 kg, we can rearrange the equation to find the velocity of the man:

Velocity of the man = Momentum of the man / mass of the man

Velocity of the man = -67.5 kg*m/s / 65 kg = -1.04 m/s

So, the velocity of the man is approximately -1.04 m/s westward.

Answer 2

The final velocity of her partner is approximately -1.04 m/s or 1.04 m/s in the opposite direction to her direction of motion

Step-by-step explanation:

The given parameters are;

The mass of the man, m₁ = 65 kg

The mass of the woman, m₂ = 45 kg

Taking the relative initial velocity of the man and the woman as 0 m/s, we have;

The initial velocity of the man, v₁₁ = 0 m/s

The initial velocity of the man, v₁₂ = 0 m/s

The final velocity of the woman, v₂₂ = 1.5 m/s

The final velocity of the man = v₂₁

Therefore, we have, by the conservation of momentum principle;

The total initial momentum = The total final momentum

Which gives;

m₁ × v₁₁ + m₂ × v₁₂ = m₁ × v₂₁ + m₂ × v₂₂

Substituting the known values;

65 × 0 + 45 × 0 = 65 × v₂₁ + 45 × 1.5

∴ 65 × v₂₁ + 45 × 1.5 = 0

45 × 1.5 = - 65 × v₂₁

v₂₁ = 45 × 1.5/(-65) ≈ -1.04 m/s

The final velocity of the man, her partner = v₂₁ ≈ -1.04 m/s.