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

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

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