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Answer:
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Work done in lifting an object is given by the equation:
[tex]\[
W = F \cdot d
\][/tex]
where:
[tex]{- \( W \) \: is \: the \: work \: done,}[/tex]
[tex]{- \( F \) \: is \: the \: force \: applied,}[/tex]
[tex]{- \( d \) \: is \: the \: distance.}[/tex]
Since the force required to lift the object is equal to its weight, we use:
[tex]\[
F = m \cdot g
\][/tex]
[tex]{- \( m \) \: is \: the \: mass \: of \: the \: object \: (10 kg),}[/tex]
[tex]{- \( g \) \: is \: the \: acceleration due \: to \: gravity \: (\( 9.8 \, \: \text{m/s}^2 \)).}[/tex]
[tex]\[
F = 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 98 \, \text{N}
\][/tex]
The distance \( d \) is given as 4 meters. Thus,
[tex]\[
W = 98 \, \text{N} \times 4 \, \text{m} = 392 \, \text{J}
\][/tex]
Power is defined as the rate at which work is done. It is given by the equation:
[tex]\[
P = \frac{W}{t}
\][/tex]
[tex]{- \( P \) \: is \: the \: power,}[/tex]
[tex]{- \( W \) \: is \: the \: work \: done \: (392 J),}[/tex]
[tex]{- \( t \) \: is \: the \: time \: taken \: (20 s).}[/tex]
[tex]\[
P = \frac{392 \, \text{J}}{20 \, \text{s}} = \boxed{19.6 \, \text{W}
\]}[/tex]