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 )

Question

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 ), 15 m, 25 m, 9 m, 12 m

MARKS App · Accepted Answer

( k ^ is given vertically upward direction) $ ​ a = − 10 m / s 2 h = − 30 m ​ A s , S=u t+\frac{1}{2} a t^2 \Rightarrow-30=5 t-\frac{1}{2} 	imes 10 	imes t^2 ⇒ t 2 − t − 6 = 0 ⇒ t = − 2 s (Not possible) or , t=32 \mathrm{~s} . T hi s i s t im e in w hi c hb o d yre a c h es t h e g ro u n d I n t hi s t im e , p ro j ec t i l e m o v in g in E a s t an d N or t h w i t h s p ee d s 3 \mathrm{~m} / \mathrm{s} an d 4 \mathrm{~m} / \mathrm{s} . D i s t an cesco v ere d in t h ese d i rec t i o n s a re ; I n e a s t (x − coor d ina t e )=3 	imes 3=9 \mathrm{~m} an d in N or t h (y − coor d ina t e )=4 	imes 3=12 \mathrm{~m} S o , P ro j ec t i l e l an d a t (x, y) \equiv(9 \mathrm{~m}, 12 \mathrm{~m}) ma r k . S o , h or i zo n t a l r an g eo f b o d yo n g ro u n d i s : im g src = " h ttp s : // c d n − q u es t i o n − p oo l . g e t ma r k s . a pp / p y q / a p e ​ am ce t / P K g X r U 0 K g T o E YW Ep 7 Z W P ​ f Sl f s w 00 q 4 y F o 6 z lMF gu RE . or i g ina l . f u ll s i ze . p n g " > b r > R an g e =\sqrt{9^2+12^2}=15 \mathrm{~m}$

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