a person sitting in a rolling chair at rest t...
a person sitting in a rolling chair at rest throws a basketball forward. since the person and the rolling chair have a greater mass than the basketball, how will the person and the rolling chair respond? they will have the same forward momentum as the basketball. they will move backward at a higher speed than the basketball moves forward. they will move backward at a lower speed than the basketball moves forward. they will travel the same distance as the basketball travels but in the opposite direction.
Answer
# Explanation:
## Step1: Recall law of conservation of momentum
The total initial - momentum of the person - chair - basketball system is zero (since they are at rest). When the person throws the basketball forward, according to the law of conservation of momentum ($p_{total - initial}=p_{total - final}$), the total final momentum must also be zero. So, the momentum of the basketball ($p_{b}=m_{b}v_{b}$) and the momentum of the person - chair system ($p_{pc}=m_{pc}v_{pc}$) are equal in magnitude and opposite in direction, i.e., $m_{b}v_{b}=-m_{pc}v_{pc}$.
## Step2: Analyze mass - speed relationship
Given that $m_{pc}>m_{b}$, from $m_{b}v_{b}=-m_{pc}v_{pc}$, we can solve for $v_{pc}=-\frac{m_{b}}{m_{pc}}v_{b}$. Since $m_{pc}>m_{b}$, the magnitude of $v_{pc}$ (speed of person - chair) is less than the magnitude of $v_{b}$ (speed of basketball). The negative sign indicates the direction is opposite. So the person and the rolling chair will move backward at a lower speed than the basketball moves forward.
# Answer:
C. They will move backward at a lower speed than the basketball moves forward.