A body is projected from the top of a tower with a velocity `baru = 3hati + 4hatj + 5hatk ms^-1, where hati, hatj and hatk` are unit vectors along east, north and vertically upwards respectively. If the height of the tower is 30m, horizontal range of the body on the ground is `(g = 10ms^-2)`

Options

A. 12m
B. 9m
C. 25m
D. 15m

Answer

D

Explanation

Answer(4) from the above figure, h= ut + 1/2 `at^2`
`Rightarrow -30 = 5t + 1/2 xx (-10) xx t^2` .
`Rightarrow -30 = 5t - 5t^2`.
`Rightarrow t^2 - t -6 = 0` .
`Rightarrow (t-3) (t+2) = 0` .
t =3 or t = 2 .
The distance covered by an projectile moving in East direction i.e, x- coordiante = `speed xxtime = 3 xx 3 =9m` similarly, The distance covered by an projectile moving in North direction i.e, y- coordinate = `4 xx3 =12m` .
Then, Range, R = `sqrt(9^2 +12^2)`.
= `sqrt(81 + 144) = sqrt225` `therefore` R = 15m.