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. 30 m
B. 45 m
C. 60 m
D. 90 m

Answer

C

Explanation

c. `u_1cos alpha = u_2cosbeta`
`30sqrt(3) = (u_(2)^(2)sin2beta)/g rArr 30sqrt(3) = (u_(2)^(2)sqrt(3))/(2g)`
`rArr u_(2)^(2) = 600 or u_2 = 10sqrt(6)`
`t_2 = (2u_2sin60^@)/g = (2(10sqrt(6))sqrt(3)//2)/10 rArr t_2 = sqrt(18)`
`u_1 = (10sqrt(6)cos60^@)/(cos30^@) = 10sqrt2`
`-h = 10sqrt(2)sin 30^@sqrt(18) - 1/2 10 (sqrt18)^2`
`=30-90 rArr h = 60m` .