A car of weight w is on inclined road, that rises by 100m over a distance of 1km and applies a constant frictional force w20  on the car.  While moving uphill on the road at a speed of 10 m/s , the car needs power p.  If it needs power  p2 while moving downhill at speed v, then value of v is

inclination of the road is tanθ=1001000  ∴       tanθ ≃sinθ  =  110  (for  very  small  value  of  θ)  situation(1)  when car is moving uphill               Power P= Force.velocity                           P =(Wsinθ +f).velocity    substitute given values here                          P=(w10⋅+w20)  10                           P  =   3w2  ---(1)                                           situation(2)   when car is moving down hill                       Power P=Force . velocity                              given power =p2   down hill              ⇒p2   =   F'.v               ⇒p2 =   (wsinθ − f) v                    substitute eqn(1) here3w4   =    (w10 − w20) v        3w4   =   w20⋅ v   ⇒   v  =    15m/sec