The force required to row a boat at constant velocity is proportional to the speed. If a speed of 4 `kmh^(-1)` requires 7.5 kW, how much power does a speed of 12 `kmh^(-1)` require?

Explanation

Let the force be `F=alpha v`, where v is speed and `alpha`is a constant of proportionality .The power required is
P=Fv=`alphav^(2)`
Let `P_(1)` be the power required for speed `v_(1)` and `P_(2)` be the power required for speed `v_(2)`.
`P_(1)=7.5 kW " and " v_(2)=3 v_(1) implies P_(2)=((v_(2))/(v_(1)))^(2) P_(1)`
`implies P_(2)=(3)^(2)xx7.5 kW =67.5 kW`