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 $\frac {W}{20}$ 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 down hill at speed $v$ then value of $v$ is $...... ms^{-1}$
JEE MAIN 2016, Difficult
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While moving downhill power
$P = \left( {w\sin \theta + \frac{w}{{20}}} \right)10$
$P = \left( {\frac{w}{{10}} + \frac{w}{{20}}} \right)10 = \frac{{3w}}{2}$
$\frac{p}{2} = \frac{{3w}}{4} = \left( {\frac{w}{{10}} - \frac{w}{{20}}} \right)V$
$\frac{3}{4} = \frac{v}{{20}} \Rightarrow v = 15m/s$
$\therefore$ Speed of car while moving downhill
$v = 15\,m/s.$
$P = \left( {w\sin \theta + \frac{w}{{20}}} \right)10$
$P = \left( {\frac{w}{{10}} + \frac{w}{{20}}} \right)10 = \frac{{3w}}{2}$
$\frac{p}{2} = \frac{{3w}}{4} = \left( {\frac{w}{{10}} - \frac{w}{{20}}} \right)V$
$\frac{3}{4} = \frac{v}{{20}} \Rightarrow v = 15m/s$
$\therefore$ Speed of car while moving downhill
$v = 15\,m/s.$
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