Two dogs were running with the same velocity after a ball. One dog was twice as large as the other. Which statement can be made about the momentum of the dogs?

Question

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Both dogs had the same momentum.
The larger dog had half the momentum of the smaller dog.
The larger dog had twice the momentum of the smaller dog.
Neither dog had momentum.

Answer 1

Momentum is calculated using the formula:

\[ \text{Momentum} (p) = \text{mass} (m) \times \text{velocity} (v) \]

Given that both dogs are running with the same velocity but one dog is twice as large (in mass) as the other, we can denote the mass of the smaller dog as \(m\) and the mass of the larger dog as \(2m\).

For the smaller dog: \[ p_{\text{small}} = m \times v \]

For the larger dog: \[ p_{\text{large}} = 2m \times v \]

This shows that the momentum of the larger dog is:

\[ p_{\text{large}} = 2(m \times v) = 2p_{\text{small}} \]

Therefore, the larger dog had twice the momentum of the smaller dog.

So, the correct statement is:

The larger dog had twice the momentum of the smaller dog.