The power of a crane, which lifts a mass of 1000 kg to a height of 20 m in 10 s is: (g = 9.8 m/s²)

The problem asks for the average power delivered by a crane that lifts a load.

First, compute the gravitational force on the mass:
$F\; =\; m\; \backslash ,\; g\; =\; 1000\backslash \; \backslash text\{kg\}\; \backslash times\; 9.8\backslash \; \backslash text\{m/s\}2=\; 9800\backslash \; \backslash text\{N\}$

The work done in raising the load through a height $h\; =\; 20\backslash \; \backslash text\{m\}$ is:
$W\; =\; F\; \backslash ,\; h\; =\; 9800\backslash \; \backslash text\{N\}\; \backslash times\; 20\backslash \; \backslash text\{m\}\; =\; 196\{,\}000\backslash \; \backslash text\{J\}$

Power is the rate at which this work is performed. With a time interval of $t\; =\; 10\backslash \; \backslash text\{s\}$, the average power is:
$P\; =\; \backslash frac\{W\}\{t\}\; =\; \backslash frac\{196\{,\}000\backslash \; \backslash text\{J\}\}\{10\backslash \; \backslash text\{s\}\}\; =\; 19\{,\}600\backslash \; \backslash text\{W\}$

Converting watts to kilowatts (1 kW = 1000 W):
$19\{,\}600\backslash \; \backslash text\{W\}\; =\; 19.6\backslash \; \backslash text\{kW\}$

Thus, the power of the crane is 19.6 kW, which matches the given correct option.