To determine the mass of the roller coaster car, we can use the relationship between momentum, mass, and velocity. The formula for momentum ([tex]\( p \)[/tex]) is given by:
[tex]\[ p = m \times v \][/tex]
where:
- [tex]\( p \)[/tex] is the momentum
- [tex]\( m \)[/tex] is the mass
- [tex]\( v \)[/tex] is the velocity
We are given:
- The momentum [tex]\( p \)[/tex] is [tex]\( 2.5 \times 10^4 \)[/tex] kilogram meters/second
- The velocity [tex]\( v \)[/tex] is 30 meters/second
We need to find the mass ([tex]\( m \)[/tex]). We can rearrange the formula to solve for mass:
[tex]\[ m = \frac{p}{v} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{2.5 \times 10^4 \, \text{kg m/s}}{30 \, \text{m/s}} \][/tex]
[tex]\[ m = \frac{25000 \, \text{kg m/s}}{30 \, \text{m/s}} \][/tex]
[tex]\[ m = 833.33 \, \text{kg} \][/tex]
The calculated mass is 833.33 kilograms, which corresponds to choice:
B. [tex]\( 8.3 \times 10^2 \)[/tex] kilograms
