Acar driving 22.7 m/s on flat ground drives off a 42.3 m high cliff. how much time does it take to reach the ground?

The horizontal 22.7 m/s doesn't make a bit of difference.  

The whole question is:  "How long does an object dropped from rest take to fall 44.3 meters ?"

To answer that, all you need is the "drop from rest" equation:

D = (1/2) · (acceleration) · (time)²

You didn't say so, but I'll assume this story all takes place on Earth, where the acceleration of gravity is 9.81 m/s².

42.3 m = (1/2) · (9.81 m/s²) · (time)²

time² = (42.3 m) / (4.91 m/s²)

time² = (42.3/4.91) s²

time = √(42.3/4.91)  seconds

time = 2.94 seconds