To determine Rita's momentum while riding the bike, we need to follow a few conceptual steps:
1. Understand the Concept of Momentum:
Momentum ([tex]\( p \)[/tex]) is calculated as the product of mass ([tex]\( m \)[/tex]) and velocity ([tex]\( v \)[/tex]):
[tex]\[
p = m \times v
\][/tex]
2. Calculate the Total Mass:
Rita's mass is 42 kilograms and the bike's mass is 7 kilograms. To find the total mass of Rita and the bike, we simply add these two values together:
[tex]\[
\text{Total Mass} = 42 \, \text{kg} + 7 \, \text{kg} = 49 \, \text{kg}
\][/tex]
3. Apply the Velocity:
Rita is riding the bike at a velocity of 15 meters/second.
4. Calculate the Momentum:
Using the formula for momentum, we can substitute the total mass (49 kg) and the velocity (15 m/s):
[tex]\[
\text{Momentum} = 49 \, \text{kg} \times 15 \, \text{m/s} = 735 \, \text{kg} \cdot \text{m/s}
\][/tex]
Given the options, we compare the calculated momentum with the closest option provided.
The correct answer is:
D. [tex]\( 7.4 \times 10^2 \)[/tex] kilogram meters/second
