A car of weight $W$ is on an inclined road that rises by $100\; m$ over a distance of $1\; km$ and applies a constant frictional force $\large\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10 ms^{−1},$ the car needs power $P$. If it needs power $\frac{P}{2}$ while moving downhill at speed $v$ then value of v is :

Question

$\begin{array}{1 1}(1) 5ms^{-1} \\ (2) 20ms^{-1} \\ (3) 10ms^{-1} \\ (4) 15 ms^{-1} \end{array}$