A truck can move up a road having a grade of $1 m$ rise in every $50 m$ with a speed of $24 km/h$ the resisting force is equal to $\frac{1}{25}$ weight of the truck. How fast will the same truck move down the hill with the same power ?

Given,  $\sin \left(\theta \right)=\frac{1}{50}$

The force needed to move the truck up the plane

               $F_1=W\sin \left(\theta \right)+\frac{W}{25}=\frac{W}{50}+\frac{W}{25}=\frac{3W}{50}$

When truck moves down the plane, force needed

                 $F_2=\frac{W}{25}-W\sin \left(\theta \right)=\frac{W}{25}-\frac{W}{50}=\frac{W}{50}$

If $v_2$ is the speed of truck down the plane, then for same power,

$$\begin{gathered} F_1{v}_1=F_2{v}_2 \\ \therefore v_2=3v_1=3\times 24=72 km/h \end{gathered}$$