Question

A basketball has a mass of 1 kg and is traveling 12 m/s. How fast would a 6 kg bowling ball have to travel to have the same momentum?

Question 5 options:

1 m/s


2 m/s


3 m/s


4 m/s

Answer 1

Momentum is calculated using the formula:

\[
\text{Momentum} = \text{mass} \times \text{velocity}
\]

First, let's calculate the momentum of the basketball:

\[
\text{Momentum of basketball} = m_b \times v_b = 1 \, \text{kg} \times 12 \, \text{m/s} = 12 \, \text{kg} \cdot \text{m/s}
\]

Now, we want to find the velocity \( v_k \) of the bowling ball that would give it the same momentum, knowing that the mass of the bowling ball \( m_k = 6 \, \text{kg} \):

\[
\text{Momentum of bowling ball} = m_k \times v_k = 6 \, \text{kg} \times v_k
\]

We set the momenta equal to each other:

\[
6 \, \text{kg} \times v_k = 12 \, \text{kg} \cdot \text{m/s}
\]

Now, we can solve for \( v_k \):

\[
v_k = \frac{12 \, \text{kg} \cdot \text{m/s}}{6 \, \text{kg}} = 2 \, \text{m/s}
\]

Thus, the bowling ball would need to travel at a speed of **2 m/s** to have the same momentum as the basketball.

The correct answer is:

**2 m/s**