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Question Number 70669 by jagannath19 last updated on 06/Oct/19

Commented by jagannath19 last updated on 06/Oct/19

$$answerwithexplanationplease$$

Commented by mr W last updated on 06/Oct/19

$$a_R=g\cos \phi$$$$\phi variesfrom\theta tozeroandfromzero$$$$to\theta ,therefore\left(a\right)or\left(c\right)couldbetrue,$$$$butthevariationof\tan \phi islinear,$$$$andthevariationof\cos \phi isnot$$$$linear,sotheonlycorrectansweris$$$$\left(a\right).$$

Commented by mr W last updated on 06/Oct/19

$$ifyouwanttogettheexactgraphfrom$$$$a_{R}withrespecttot:$$$$x=v_0\cos \theta t$$$$y=v_0\sin \theta t-\frac{1}{2}{gt}^2$$$$\tan \phi =\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{v_0\sin \theta -gt}{v_0\cos \theta }=\tan \theta -\frac{gt}{v_0\cos \theta }$$$$\cos \phi =\frac{1}{\sqrt{1+{\tan }^2\phi }}=\frac{1}{\sqrt{1+{(\tan \theta -\frac{gt}{v_0\cos \theta })}^2}}$$$$a_R=g\cos \phi$$$$a_R=\frac{g}{\sqrt{1+{(\tan \theta -\frac{gt}{v_0\cos \theta })}^2}}$$$$thegraphof{a}_{R}w.r.t.tseefollowing$$$$example:$$

Commented by mr W last updated on 06/Oct/19

Commented by jagannath19 last updated on 07/Oct/19

$$thankyousomuchsir$$

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