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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 after grazing the vertex falls on the other end of the base. If `alpha and beta` be the base angles and `theta` the angle of projection, prove that `tan theta = tan alpha + tan beta` .

Text Solution

Verified by Experts

The correct Answer is:
A
The situation is shown in figure.

From figure, we have
`tan alpha + tan beta = y/x + y/(R-x)`
`tan alpha + tan beta = (yR)/(x(R-x))`……….(i)
Equation of trajectory is
`y = x tan theta [1-x/R]`
or, ` tan theta = (yR)/(x(R-x))` ........(ii)
From Eqs. (i) and (ii), we have
`tan theta = tan alpha + tan beta`
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