Which of the following objects has the largest momentum relative to $\mathrm{Earth}$?

• A. A $1000\mathrm{kg}$ car moving at $30m/s$
• B. A $0.1\mathrm{kg}$ baseball moving at $40m/s$
• C. A $70\mathrm{kg}$ person running at $5m/s$
• D. A $2\mathrm{kg}$ book dropped from rest

Answer: (A)

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. Identify the mass and velocity for each object from the problem: - Car: \(m = 1000\,\text{kg}\), \(v = 30\,\text{m/s}\) - Baseball: \(m = 0.1\,\text{kg}\), \(v = 40\,\text{m/s}\) - Person: \(m = 70\,\text{kg}\), \(v = 5\,\text{m/s}\) - Book: \(m = 2\,\text{kg}\), dropped from rest, so \(v = 0\,\text{m/s}\) initially
3. Calculate the momentum for each object by multiplying their mass and velocity: - \(p_{\text{car}} = 1000 \times 30\) - \(p_{\text{baseball}} = 0.1 \times 40\) - \(p_{\text{person}} = 70 \times 5\) - \(p_{\text{book}} = 2 \times 0\)
4. Compare the calculated momentum values to determine which object has the largest momentum relative to Earth.
5. Conclude that the object with the greatest product of mass and velocity has the largest momentum.