Answer :
To determine Naoki's mass, we can use Newton's Second Law of Motion, which states that force equals mass times acceleration (F = ma).
We are given:
- The force exerted by Naoki: [tex]F = 126 \text{ N}[/tex]
- The total mass of the system when Naoki is on the bicycle: [tex]m_{total}[/tex]
- The acceleration: [tex]a = 2 \text{ m/s}^2[/tex]
- The mass of the bicycle itself: [tex]9 \text{ kg}[/tex]
First, we can rearrange the formula to solve for the total mass:
[tex]m_{total} = \frac{F}{a}[/tex]
Plug in the known values:
[tex]m_{total} = \frac{126}{2}[/tex]
[tex]m_{total} = 63 \text{ kg}[/tex]
This [tex]m_{total}[/tex] includes both Naoki's mass and the mass of the bicycle. Since we know the bicycle's mass is 9 kg, we can solve for Naoki's mass ([tex]m_{Naoki}[/tex]):
[tex]m_{Naoki} = m_{total} - \text{mass of bicycle}[/tex]
[tex]m_{Naoki} = 63 \text{ kg} - 9 \text{ kg}[/tex]
[tex]m_{Naoki} = 54 \text{ kg}[/tex]
So, the correct answer is:
B. 54 kg
