A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 ms^-1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s^-2).

Question

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 ms^-1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s^-2).

Philoid · Accepted Answer

Here the plane will move forward in horizontal direction in some time t and shell will cover the same horizontal distance along with reach the altitude or height of the plane

Now this is the case of projectile motion, the motion of Shell will be a projectile and its path will be parabola, the motion of shell can be divided into horizontal component and vertical component i.e. motion along x axis and motion along y axis

Initial speed of shell is u = 600 m/s

And let it be making an angle