An arrow was shot horizontally at a speed of 40 m/s from a bow held 1.5 meters above the ground. It misses the target and hits the ground how much time does it take the arrow to hit the ground?

If we can ignore any effects of air resistance ... and we always do ... then it makes no difference what its horizontal speed was, or whether it had any at all.  It hits the ground in the same time as an arrow that just dropped from the bow to ground.The distance an object falls from rest in ' T ' seconds, on account of gravity, is         D  =  1/2 G T² .            ('G' is the acceleration of gravity, 9.8m/s² )This arrow falls 1.5 meters,and 1/2 G is  9.8/2  =  4.9 m/s² .       1.5 m  =  4.9 m/s²  T²Divide each side by  4.9 m/s² :    (1.5 / 4.9)  sec²  =  T²Take the square root of each side:    T  =  square root of (1.5/4.9) = 0.553 sec