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

There are two parallel planes, each inclined to the horizontal at an angle θ. 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 strikes the other at right angle. Find the angle of projection of the projectile.

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

Commented by Tinkutara last updated on 17/Jul/17

Commented by Tinkutara last updated on 01/Aug/17

The point is midpoint of the line joining feet of the two planes (as not shown in the figure).

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

Commented by ajfour last updated on 03/Aug/17

I have a method but that fetches correct answer but in another form. φ=tan^(−1) [tan θ+(1/(√2))(tan θ+cot θ)].

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

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