There-are-two-parallel-planes-each-inclined-to-the-horizontal-at-an-angle-A-particle-is-projected-from-a-point-mid-way-between-the-foot-of-the-two-planes-so-that-it-grazes-one-of-the-planes-and-st

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Question Number 18271 by Tinkutara last updated on 01/Aug/17

$$\mathrm{There}\mathrm{are}\mathrm{two}\mathrm{parallel}\mathrm{planes},\mathrm{each}$$$$\mathrm{inclined}\mathrm{to}\mathrm{the}\mathrm{horizontal}\mathrm{at}\mathrm{an}\mathrm{angle}\theta .$$$$\mathrm{A}\mathrm{particle}\mathrm{is}\mathrm{projected}\mathrm{from}\mathrm{a}\mathrm{point}\mathrm{mid}$$$$\mathrm{way}\mathrm{between}\mathrm{the}\mathrm{foot}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{planes}$$$$\mathrm{so}\mathrm{that}\mathrm{it}\mathrm{grazes}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{planes}\mathrm{and}$$$$\mathrm{strikes}\mathrm{the}\mathrm{other}\mathrm{at}\mathrm{right}\mathrm{angle}.\mathrm{Find}$$$$\mathrm{the}\mathrm{angle}\mathrm{of}\mathrm{projection}\mathrm{of}\mathrm{the}\mathrm{projectile}.$$

Commented by Tinkutara last updated on 17/Jul/17

Commented by Tinkutara last updated on 01/Aug/17

$$\mathrm{The}\mathrm{point}\mathrm{is}\mathrm{midpoint}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{joining}$$$$\mathrm{feet}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{planes}(\mathrm{as}\mathrm{not}\mathrm{shown}\mathrm{in}$$$$\mathrm{the}\mathrm{figure}).$$

Commented by ajfour last updated on 03/Aug/17

$$\mathrm{I}\mathrm{have}\mathrm{a}\mathrm{method}\mathrm{but}\mathrm{that}\mathrm{fetches}$$$$\mathrm{correct}\mathrm{answer}\mathrm{but}\mathrm{in}\mathrm{another}\mathrm{form}.$$$$\varphi ={\tan }^{-1}[\tan \theta +\frac{1}{\sqrt{2}}(\tan \theta +\cot \theta )].$$

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