College

A large truck is moving at [tex]$22.0 \, \text{m/s}$[/tex]. If its momentum is [tex]$125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}$[/tex], what is the truck's mass?

A. 176 kg
B. 2750 kg
C. 5680 kg
D. [tex]11,400 \, \text{kg}[/tex]

Answer :

To find the truck's mass, we need to use the relationship between momentum, mass, and velocity. The formula for momentum ([tex]\( p \)[/tex]) is:

[tex]\[ p = m \times v \][/tex]

where [tex]\( p \)[/tex] is momentum, [tex]\( m \)[/tex] is mass, and [tex]\( v \)[/tex] is velocity.

We are given:
- Momentum ([tex]\( p \)[/tex]) = 125,000 kg·m/s
- Velocity ([tex]\( v \)[/tex]) = 22.0 m/s

We need to solve for mass ([tex]\( m \)[/tex]). Rearrange the formula to solve for [tex]\( m \)[/tex]:

[tex]\[ m = \frac{p}{v} \][/tex]

Substitute the given values into the equation:

[tex]\[ m = \frac{125,000 \, \text{kg·m/s}}{22.0 \, \text{m/s}} \][/tex]

When you perform the division, you get:

[tex]\[ m \approx 5681.82 \, \text{kg} \][/tex]

So, the nearest approximate mass of the truck is 5680 kg.