To determine the power Carter uses while pushing the bag full of basketball jerseys across the gym floor, we need to follow a two-step process.
Step 1: Calculate the work done (W).
Work is defined as the product of the force applied and the distance over which the force is applied. The formula for work is:
[tex]\[ W = F \cdot d \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied (in newtons, [tex]\( N \)[/tex])
- [tex]\( d \)[/tex] is the distance over which the force is applied (in meters, [tex]\( m \)[/tex])
Given:
- Force, [tex]\( F = 21 \, \text{N} \)[/tex]
- Distance, [tex]\( d = 9 \, \text{m} \)[/tex]
Let's calculate the work done:
[tex]\[ W = 21 \, \text{N} \times 9 \, \text{m} = 189 \, \text{J} \][/tex]
The work done by Carter is [tex]\( 189 \)[/tex] joules ([tex]\( J \)[/tex]).
Step 2: Calculate the power (P).
Power is defined as the rate at which work is done, which can be calculated by dividing the work done by the time taken. The formula for power is:
[tex]\[ P = \frac{W}{t} \][/tex]
where:
- [tex]\( W \)[/tex] is the work done (in joules, [tex]\( J \)[/tex])
- [tex]\( t \)[/tex] is the time taken (in seconds, [tex]\( s \)[/tex])
Given:
- Work done, [tex]\( W = 189 \, \text{J} \)[/tex]
- Time, [tex]\( t = 3 \, \text{s} \)[/tex]
Let's calculate the power:
[tex]\[ P = \frac{189 \, \text{J}}{3 \, \text{s}} = 63 \, \text{W} \][/tex]
Therefore, the power Carter uses is [tex]\( 63 \)[/tex] watts ([tex]\( W \)[/tex]).
Answer: The correct option is
[tex]\[ \boxed{63 \, \text{watts}} \][/tex]
