An enemy plane is flying horizontally at an altitude of 2km witha speed of 300ms^(-1). An army man with an anti-aircraft gun on the ground sights hit enemy plane when it is directly overhead and fires a shell with a muzzle speed of 600ms^(-1). At what angle with the vertical should the gun be fired so as to hit the plane ?

An enemy plane is flying horizontally at an altitude of 2km witha spee

1.	An enemy plane is flying horizontally at an altitude of 2km witha speed of 300ms^(-1). An army man with an anti-aircraft gun on the ground sights hit enemy plane when it is directly overhead and fires a shell with a muzzle speed of 600ms^(-1). At what angle with the vertical should the gun be fired so as to hit the plane ?
Answer» <P> Solution :LET G be the position of the gun and E that of the enemy plane flying horizontally with speed ` u = 300ms^(-1)`, when the shell is fired with a speed `v_(0)` is `v_(x) = v_(0)costheta` Let the shell hit the plane a point P and let t be the time taken for the shell to hit plane. It is clear that the shell will hit the plane, if the horizontal distance EP travelled by the plane in time t = the distance travelled by the shell in the horizontal direction in the same time, i.e. `uxxv = v_(x)XXT or u= v_(x) = v_(0) costheta` ` or costheta = (u)/(v_(0)) = (300)/(600)` `=0.5 or theta = 60^(0)`. Therefore, angle with the vertical = `90^(0)-theta=30^(0)`.