Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation `alpha = 30^@`, beta `= 60^@`, respectively. The shots strike an object simultaneously at the same point. If `a = 10 (sqrt3)` m is the horizontal distance of the object from the cliff, then the height h of the cliff is

Options

A. `(a(cotalpha-cotbeta))/(cotalphacot 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 origins 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)`
`:. -m=a tan alpha- ("ga"^(2))/(2u^(2)cos^(2)beta)`
`:.(m+n)=alpha(tan beta-tan alpha)`
because `u cos alpha=v cos beta` because both the shots reach `P` simultaneously.This is possible only if the horizontal components of the velocities are equal.