Shots are fired simu ltaneou ly from the top and bottom of a vertical cliff at angles `alpha` and `beta` and they stike an object simu ltaneously at the same point. If the horizontal distance of the object from the cliff is a, the height of the dcliff is :

Options

A. `(a(cot alpha-cot beta))/(cot alpha cot beta)`
B. `a(sin beta-tan alpha)`
C. `(a tan alpha)/(tan beta)`
D. `a(cot alpha-cot beta)`

Answer

a

Explanation

Coordinates of P w.r.t. O and O' as orgins are (a,n) and (a,-m). The height of the cliff =h=m+n.
`y=x tan alpha-(gx^(2))/(2u^(2)cos^(2)alpha)`
`therefore -m=a tan alpha-(ga^(2))/(2u^(2)cos^(2)alpha)`
`v_(0)=sqrt((2gh)/(2+cot^(2)theta)), -n=a tan beta-(ga^(2))/(2v^(2)cos^(2)beta)`
`therefore (m+n)=a(tan beta-tan alpha)`
because `u cos alpha=v cos beta` because both the shots reach P simu ltaneously. This is possible only if the horizontal components of the velocities are equal.