To find the speed of the boy and the skateboard, we can use the basic equation from physics that relates momentum, mass, and speed. The formula to compute speed ([tex]\(v\)[/tex]) is given by:
[tex]\[ v = \frac{p}{m} \][/tex]
where:
- [tex]\( p \)[/tex] is the momentum,
- [tex]\( m \)[/tex] is the mass.
Given:
- The momentum ([tex]\( p \)[/tex]) is [tex]\( 275 \, \text{kg} \cdot \frac{m}{s} \)[/tex],
- The combined mass ([tex]\( m \)[/tex]) of the boy and the skateboard is [tex]\( 65 \, \text{kg} \)[/tex].
Plugging the values into the formula, we get:
[tex]\[ v = \frac{275 \, \text{kg} \cdot \frac{m}{s}}{65 \, \text{kg}} \][/tex]
Performing the division gives:
[tex]\[ v \approx 4.230769230769231 \, \text{m/s} \][/tex]
Rounding to one decimal place, we find that the speed is approximately [tex]\( 4.2 \, \text{m/s} \)[/tex].
So, the correct answer is:
[tex]\[ 4.2 \, \text{m/s} \][/tex]
