A body is projected from the top of a tower with a velocity u =3 i +4 j +5 k ms ⁻¹ , where i , j and k are unit vectors along east, north and vertically upwards respectively. If the height of the tower is 30 ~m , horizontal range of the body on the ground is (g=10 ~ms ⁻² )

Step-by-step solution

( k is given vertically upward direction) aligned & a=-10 ~m / s ^2 & h=-30 ~m aligned As, S=u t+ 1 2 a t^2 -30=5 t- 1 2 10 t^2 t^2-t-6=0 t=-2 s (Not possible) or, t=32 ~s . This is time in which body reaches the ground In this time, projectile moving in East and North with speeds 3 ~m / s and 4 ~m / s . Distances covered in these directions are; In east (x - coordinate )=3 3=9 ~m and in North (y - coordinate )=4 3=12 ~m So, Projectile land at (x, y) (9 ~m , 12 ~m ) mark. So, horizontal range of body on ground is: