Question

select the correct answer.
a roller coaster car moving at a velocity of 30 meters/second has a momentum of $2.5 \times 10^4$ kilogram meters/second. what is its mass?
a. 85 kilograms
b. $8.3 \times 10^2$ kilograms
c. $7.6 \times 10^2$ kilograms
d. $7.6 \times 10^3$ kilograms
e. $7.6 \times 10^4$ kilograms

Explanation:

Step1: Recall the momentum formula

The formula for momentum \( p \) is \( p = mv \), where \( m \) is mass and \( v \) is velocity. We need to solve for \( m \), so rearrange the formula to \( m=\frac{p}{v} \).

Step2: Substitute the given values

We know \( p = 2.5\times 10^{4}\space kg\cdot m/s \) and \( v = 30\space m/s \). Substitute these into the formula: \( m=\frac{2.5\times 10^{4}}{30} \).

Step3: Perform the division

Calculate \( \frac{2.5\times 10^{4}}{30}=\frac{25000}{30}\approx 833.33 \), which is \( 8.3\times 10^{2}\space kg \) (since \( 833.33\approx 8.3\times 10^{2} \)).

Answer:

B. \( 8.3 \times 10^{2} \) kilograms