A fighter plane fly horizontaly at an altitude of 1 5km with the speed 720km/hr passes directly over here, - Physics - Motion In A Plane

Question

A fighter plane fly horizontaly at an altitude of 1 5km with the
speed 720km/hr passes directly over here, an anti aircraft gun
At what anglefrom the vertically should the gun be fired for the
shell with muzzle speed 600m/s to hit the plane At what minimum
altitude should a piolet fly to avoid being hit?

nitish.gupta · Accepted Answer

Consider O be the position of the gun and A be the position of the plane:

The speed of the plane, v = 720 km/h or 200 m/s The speed of the shell, u = 600 m/s Let the shell hit the plane at B after time t if fired at an angle Î¸ with the vertical from O The horizontal distance travelled by shell in the time t is the same as the distance covered by the plane $u_{x} \times t = v t$ or $u \sin θ t = v t$ sin Î¸ = v/u = 0 3333 or â‡’ Î¸ = 19 5Â° with the vertical The plane will not be hit by the bullet from the gun if it is flying at a minimum height which is the maximum height (H) attained by the bullet after firing from gun here $H = \frac{u^{2} \sin^{2} (90^{0} - θ)}{2 g} = \frac{u^{2} \cos^{2} θ}{2 g}$ substituting the values we get, H = 16000 m or 16 km Hope it helps!