Question 162 of 183

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

A$20m{s}^{-1}$B$5m{s}^{-1}$C$15m{s}^{-1}$D$10m{s}^{-1}$

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Answer: (C) $15m{s}^{-1}$

$P=\left(w\sin ⁡\theta +\dfrac{w}{20}\right)10$

$P=\left(\dfrac{w}{10}+\dfrac{w}{20}\right)10=\dfrac{3w}{2}$



$\dfrac{P}{2}=\dfrac{3w}{4}=\left(\dfrac{w}{10}-\dfrac{w}{20}\right)v$

$\dfrac{3}{4}=\dfrac{v}{20}$

$15m/s=v$