Question

A basketball has a mass of 1 kg and is traveling 15 m/s. How fast would a 5 kg bowling ball have to travel to have the same momentum?

Question 5 options:

1 m/s


3 m/s


5 m/s


15 m/s

Answer 1

Momentum is calculated using the formula:

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

First, we find the momentum of the basketball:

\[
\text{Momentum}_{\text{basketball}} = 1\, \text{kg} \times 15\, \text{m/s} = 15\, \text{kg m/s}
\]

To find the velocity of the bowling ball that would give it the same momentum, we can set the momentum of the bowling ball equal to the momentum of the basketball:

\[
\text{Momentum}_{\text{bowling ball}} = \text{mass} \times \text{velocity} = 5\, \text{kg} \times v
\]

Setting the two momenta equal:

\[
15\, \text{kg m/s} = 5\, \text{kg} \times v
\]

Now, we solve for \(v\):

\[
v = \frac{15\, \text{kg m/s}}{5\, \text{kg}} = 3\, \text{m/s}
\]

Thus, the bowling ball would need to travel at **3 m/s** to have the same momentum as the basketball.

So, the answer is:

**3 m/s**