A projectile is fired with velocity `v_(0)` from a gun adjusted for a maximum range.It passes through two points `P` and `Q` whose heights above the horizontal are `h` each.The separation of the two points is

Options

A. `v_(0)/gsqrt(v_(0)^(2)-4 gh)`
B. `v_(0)/gsqrt(v_(0)^(2)+4 gh)`
C. `2v_(0)/gsqrt(v_(0)^(2)-4 gh)`
D. `v_(0)/gsqrt(v_(0)^(2)- gh)`

Answer

A

Explanation

Gun is adjusted for maximum range, therefore `alpha=45^(@)`
`y=x-gx^(2)/v_(0)^2 or x^(2)-v_(0)^2/gx+v_(0)^2/gh=0`
If `x_(1)` and `x_(2)` are roots of the above equation
`x_(1)+x_(2)=v_(0)^(2)/g and x_(1)x_(2)=v_(0)^(2)/h`
`(x_(1)-x_(2))^(2)=(x_(1)+x_(2))^(2)-4x_(1)x_(2)`
`=(v_(0)^(2)/g)^(2)-4v_(0)^(2)/gh , x_(1)-x_(2)=v_(0)^(2)/gsqrt(v_(0)^(2)-4gh)`