Which object has more momentum: a $2\mathrm{kg}$ ball moving at $3m/s$ or a $1\mathrm{kg}$ ball moving at $6m/s$?

• A. Both have the same momentum
• B. The $1\mathrm{kg}$ ball moving at $6m/s$
• C. It cannot be determined without knowing the direction
• D. The $2\mathrm{kg}$ ball moving at $3m/s$

Answer: (D)

Verified step by step guidance

1. Recall that momentum \(p\) is defined as the product of an object's mass \(m\) and its velocity \(v\), given by the formula: \(p = m \times v\)
2. Calculate the momentum of the 2 kg ball moving at 3 m/s by substituting the values into the formula: \(p_1 = 2 \text{ kg} \times 3 \text{ m/s}\)
3. Calculate the momentum of the 1 kg ball moving at 6 m/s similarly: \(p_2 = 1 \text{ kg} \times 6 \text{ m/s}\)
4. Compare the two momentum values \(p_1\) and \(p_2\) to determine which is greater.
5. Conclude which ball has more momentum based on the comparison of \(p_1\) and \(p_2\).