What is the speed of projection of a particle which strikes the roof of building at B at an angle of 30° with the horizontal, after being projected from point A towards a building of height h as shown at an angle of 60° with horizontal ?

Options

A. `sqrt(gh)`
B. `sqrt(2gh)`
C. `sqrt(3gh)`
D. `root(2)(gh)`

Answer

C

Explanation

Let u be the speed of projection and v be the speed at B
`u cos 60^(@) = v cos 30^(@)`
`rArr v = u/sqrt(3)` .............. (i)
Applying law of conversation of energy.
`1/2 mv^(2) - 1/2 mu^(2) =-mgh`...... (ii)
Using equation (i) in equation (ii), we have `u = sqrt(3gh)`