A truck can move up a road having a grade of 1.0 m rise for every 50 m with a speed of `18(km)//(h)`. The resisting force is equal to `(1)//(25)` of the weight of the truck. With what speed the same truck moves down the hill with the same power?

Explanation

`sintheta=(1)/(50)`
Since the truck moves with a constant speed
`F=Wsintheta+f=(W)/(50)+(W)/(25)=(3W)/(50)`
Power of engine
`P=Fv=(3W)/(50)xx18`.(i)

`F^(')=Wsintheta=f`
`F^(')+(W)/(50)=(W)/(25)impliesF^(')=(W)/(25)` .(ii)
Equating (i) and (ii) we get
`(3W)/(50)xx18=(W)/(25)v^(')`
`v^(')=27(km)/(h)`