An airplane flying horizontally at a height h and speed j is to be shot down by a gun firing a shell with initial muzzle velocity v at an angle θ with the horizontal. Find the condition for the shell

You're on a roll — Step 1: Define the motion of the airplane and the shell. Let the origin be at the gun's position. The airplane flies at a constant height h and constant speed j. The shell is fired with an initial muzzle velocity v at an angle with the horizontal. Let t be the time from firing until the shell hits the airplane. Step 2: Analyze the horizontal motion. The horizontal distance covered by the airplane in time t is x_A = j t. The horizontal component of the shell's initial velocity is v_x = v . The horizontal distance covered by the shell in time t is $x_S