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Question Number 37652 by Rio Mike last updated on 16/Jun/18

A car,of mass 1000kg,has an engine capable of developing power of 15Kw against a constand Resistance R N.The maximum speed of the car on level road is ((100)/3) ms^(−1) Calculate the value of R. Given that the resistance and the power remain unchanged find the maximum speed of the car up a plane which is inclinded at an angle θ to the horizontal,where Sin θ= (1/(25)).

$$\mathrm{A}\:\mathrm{car},\mathrm{of}\:\mathrm{mass}\:\mathrm{1000kg},\mathrm{has}\:\mathrm{an}\:\mathrm{engine} \\ $$$$\mathrm{capable}\:\mathrm{of}\:\mathrm{developing}\:\mathrm{power}\:\mathrm{of}\: \\ $$$$\mathrm{15Kw}\:\mathrm{against}\:\mathrm{a}\:\mathrm{constand}\:\mathrm{Resistance} \\ $$$$\mathrm{R}\:\mathrm{N}.\mathrm{The}\:\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car} \\ $$$$\mathrm{on}\:\mathrm{level}\:\mathrm{road}\:\mathrm{is}\:\frac{\mathrm{100}}{\mathrm{3}}\:{ms}^{−\mathrm{1}} \: \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{R}. \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{and}\:\mathrm{the}\:\mathrm{power} \\ $$$$\mathrm{remain}\:\mathrm{unchanged} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car} \\ $$$$\mathrm{up}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{which}\:\mathrm{is}\:\mathrm{inclinded}\:\mathrm{at}\:\mathrm{an} \\ $$$$\mathrm{angle}\:\theta\:\mathrm{to}\:\mathrm{the}\:\mathrm{horizontal},\mathrm{where}\: \\ $$$$\mathrm{Sin}\:\theta=\:\frac{\mathrm{1}}{\mathrm{25}}. \\ $$

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