Water falls from a height of $60\, m$ at the rate of $15\, kg/s$ to operate a turbine. The losses due to frictional forces are $10\%$ of energy. How much power is generated by the turbine ............. $kW$ ? $(g = 10\, m/s^2)$

The blades of a windmill sweep out a circle of area $A$.
$(a)$ If the wind flows at a velocity $v$ perpendicular to the circle,what is the mass of the air passing through it in time $t?$
$(b)$ What is the kinetic energy of the air?
$(c)$ Assume that the windmill converts $25\%$ of the wind's energy into electrical energy,and that $A=30\;m^{2}, v=36\;km/h$ and the density of air is $1.2\;kg\;m^{-3}.$ What is the electrical power produced?

$A$ force of $(2\hat{i} + 3\hat{j} + 4\hat{k})\,N$ acts on a body for $4\,s$ and produces a displacement of $(3\hat{i} + 4\hat{j} + 5\hat{k})\,m$. The power used is :- ............... $W$ (in $.5$)

What average horsepower is developed by an $80 \; kg$ man while climbing in $10 \; s$ a flight of stairs that rises $6 \; m$ vertically?

$A$ force of $5 \,N$ acts on a body initially at rest. If the instantaneous power due to the force at the end of the third second $(t=3 \,s)$ is $5 \,W$, then the mass of the body is (in $\,kg$)

$A$ man does a given amount of work in $10 \ s$. Another man does the same amount of work in $20 \ s$. The ratio of the output power of the first man to the second man is: