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 :