A fighter plane flying horizontally at an altitude of `1.5 km ` with speed of `720 km h^9-10` passes directlu overhead an anticraft gun. At what anle fro the gun with muzzle speed ` 400 ms^(-1)` to hit the plane in shortest time ?`

Options

A. `sin^(-1)(1/3)`
B. `sin^(-1)(2/3)`
C. `cos^(-1)(1/3)`
D. `cos^(-1)(2/3)`

Answer

a

Explanation

Here, Speed of the plane, `v=720kmh^(-1)`
`720xx5/18ms^(-1)=200ms^(-1)`
Speed of the shell , `u=600ms^(-1)`
Let the shell will hit the plane of L after time t if fired at an angle `theta` with the vertical from O.
For hitting, horizontal distance travelled by the plane =horizontal distance travelled by the shell.
i.e,. `vxxt=u sin thetaxxt`
`sin theta=v/u=(200ms^(-1))/(600ms^(-1))=1/3`
`theta=sin^(-1)(1/3)`