To determine the speed of the boy and his skateboard, we need to use the relationship between momentum, mass, and velocity. The formula for momentum ([tex]\( p \)[/tex]) is given by:
[tex]\[ p = m \cdot v \][/tex]
where:
- [tex]\( p \)[/tex] is the momentum,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( v \)[/tex] is the velocity (or speed).
Given the values:
- The combined mass of the boy and skateboard ([tex]\( m \)[/tex]) is [tex]\( 65 \, \text{kg} \)[/tex].
- The momentum ([tex]\( p \)[/tex]) is [tex]\( 275 \, \text{kg} \cdot \frac{m}{s} \)[/tex].
We need to solve for the speed ([tex]\( v \)[/tex]). Rearrange the momentum formula to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \frac{p}{m} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ v = \frac{275 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{65 \, \text{kg}} \][/tex]
[tex]\[ v = 4.230769230769231 \, \frac{\text{m}}{\text{s}} \][/tex]
Therefore, the speed of the boy and skateboard is approximately [tex]\( 4.2 \, \frac{\text{m}}{\text{s}} \)[/tex].
Among the given options, the correct one is:
[tex]\[ \boxed{4.2 \, \frac{\text{m}}{\text{s}}} \][/tex]
