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

Hint : Force on the truck when it moves down the hill is
`F.=mg sin theta-mu_(k)mg cos theta`
Power, `P=F..V.` calculate v.
Force on the truck when it moves down the hill
`F.=mg sin theta-mu_(k)mg cos theta`
`=mg(sin theta-mu_(k))("taking "cos theta=1" as angle is very small")`
`=10^(5)((1)/(50)-0.2)`
`=10^(5)((-9)/(50))=-18,000N`
Negative sign signifies direction
Power = F..v.
`22xx10^(4)=18000v`
`v=(220)/(18)=12.2ms^(-1)`
`=12.2xx(18)/(5)=43.99`
`=44kmh^(-1)`