An object is launched from a cliff 20m above the ground at an angle of `30^(@)` above the horizontal with an initial speed of 30m/s. How far horizontally does the object travel before landing on the ground ? `(g = 10 m//s^(2))`

Explanation

`h = 20m, theta = 30^(@), u = 30m//s, g = 10m//s^(2)`
`h = -(u sin theta) t + (1)/(2) g t^(2)`
`20 = -30 sin 30^(@) xx t + (1)/(2) xx 10 xx t^(2)`
`20 = -30 xx (1)/(2) xx t + (1)/(2) xx 10 xx t^(2)`
`4 = -3t + t^(2)`
`t^(2) - 3t - 4 = 0`
`(t - 4)(t+1) = 0`
t = 4 sec (or) t = -1 sec

`therefore` Range (R) `= u cos theta xx t`
`= 30 cos 30^(@) xx 4`
`= 30 xx (sqrt(3))/(2) xx 4`
`R = 60 sqrt(3)m`