A gun kept on a striaght horizontal is used to hit a car, traveling along the same road away form the gun with a unfrom speed `20 m//s`. The car is at a distance 0f `160 m` from the gun, when the gun is fired at an angle of `45^(@)` with the horizontal Find the distance of the car from the gun when the shell hits it and the speed of projection of the shell from the gun.

Explanation

Guns is fired from `O` and the car is at `A`. The shell will hit the car at point `B`, after the time of flight of shell `T`.
`R = 160 + d`
`(u^(2))/(g)sin (2 xx 45^(@)) = 160 + v_(0)T = 160 + v_(0) xx (2u sin 45^(@))/(g)`
`(u^(2))/(g) = 160 + 20 xx (sqrt(2) u)/(g)`
`u^(2) - 20sqrt(2)u - 1600 = 0`
`u = (20sqrt(2)+- sqrt(800 + 6400))/(2) = (20sqrt(2) +- 60sqrt(2))/(2)`
`= 40 sqrt(2) m//s`
`= -20 sqrt(2) m//s` (not possible)
`R = (u^(2))/(g) = ((40 sqrt(2))^(2))/(10) = 320 m`
Distance of the car from the gun when the shell hits is `320 m`.
Speed of projection of the shell `= 40 sqrt(2) m//s`.