Question

an ice skater at rest on ice catches a dance partner moving 2.5m/s during a performance. the ice skater has a mass of 68kg and the dance partner has a mass of 54kg. what is the speed of the ice skater and dance partner after the collision ?

1.1 m/s
1.4 m/s
2.3 m/s
2.0 m/s

Answer 1

The final velocity of the ice skater and dance partner after the collision is 1.1 m/s.

The given parameters;

• mass of the ice skater, m₁ = 68 kg
• mass of the dance partner, m₂ = 54 kg
• initial velocity of the dance partner, u₂ = 2.5 m/s
• initial velocity of the ice skater, u₁ = 0

The final velocity of the ice skater and dance partner after the collision is calculated by applying the principle of conservation of momentum;

$m_1 u_1 + m_2 u_2 = v(m_1 + m_2)\\\\68(0) + 54(2.5) = v(54 + 68)\\\\135 = 122 v\\\\v = \frac{135}{122} \\\\v = 1.1 \ m/s$

Thus, the final velocity of the ice skater and dance partner after the collision is 1.1 m/s.

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