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A particle is thrown over a triangle fro...

A particle is thrown over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. If `alpha and beta` be the base angles and `theta` be the angle of projection, prove thattam `theta=tanalpha+tanbeta`.

Text Solution

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The situation is shown in figure. From figure, we have

`tanalpha+tanbeta=(y)/(x)+(y)/(R-x)`
`tanalpha+tanbeta=(yR)/(x(R-x))" "…….(i)`
But equation of trajectory is `y = xtantheta[1-(x)/(R)]`
`tantheta=(yR)/(x(R-x))" "...........(ii)`
From Eqs. (i) and (ii),`tantheta=tanalpha+tanbeta`
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