A gun is mounted on a plateau 960 m away from its edge as shown. Height of plateau is 960 m The gun can fire shells with a velocity of 100 m/s at any angle. Of the following choices, what is the minimum distance (OP)x from the edge of plateau where the shell of gun can reach?

Options

A. 480m
B. 720m
C. 360m
D. none

Answer

A

Explanation

`P is pointon plane for shell when it passes near edge of plateau for greater angle of projection in region AP shell cannot hit
`x_(max)=AP`
Equation of trajectory for projectile
` y=xtan0-(gx)^(2)/(2u^(2))(1+tan^(2)0)`
for point E `y=0` & `x=960` m
`1 Rightarrow tan^(2)0xx(10xx(960)^(2))/(2xx(100)^(2))-(tan0)x+(10xx960^(2))/(2xx(100)^(2))=0`
` tan0=3//4,4//3for tan0=4//3` APis least Now equation of trajectory becomes
`y=4/3x-x^(2)/2000(25/9)`
for landing point on plane (p) `y=-960` m
` Rightarrow -960=4/3x-x^(2)/720`
solving we get acceptable solution `x=1440` m
`AP=x-960=480m]`