An object is thrown from a point 'A' horizontally from a tower and hits the ground 3s later at B. The line from 'A' to 'B' makes an angle of `30^(@)` with the horizontal. The initial velocity of the object is `15sqrt(x)m//s`. Find x : (take `g=10m//s^(2)`)

Options

A. `15 sqrt 3 " m/s"`
B. `15" m/s"`
C. `10 sqrt 3" m/s"`
D. `25// sqrt 3" m/s"`

Answer

A

Explanation

`AC=(1)/(2)"gt"^(2)=45" m"` `BC= 45 sqrt 3" "m= 11`
`u=(45)/sqrt 3= 15 sqrt 3 " m/s".`
Alter : Object is thrown horizontally so `u_(k)=v` From Diagram
`y=u_(r) t-(1)/(2)g" "t^(2)`
`y =(1)/(2) xx 10 xx 3^(2)`
y = 45 m .................. (a)
`& tan 30 ^(@) =(y)/(x)implies y sqrt 3 = x ....... (b)`
`& x = v t = 3v" "............(c)`

From equation (a), (b) & (c)
`45 sqrt 3 = 3v`
`v = 15 sqrt 3 " m/s"`