Final answer:
The time the arrow is in the air after being shot horizontally from a 20 m high cliff is approximately 2.02 seconds, and the horizontal range of the arrow is approximately 80.8 meters.
Step-by-step explanation:
An archer shoots an arrow horizontally at a speed of 40 m/s from a 20 m high cliff. To determine the arrow's time in the air, we can use the formula t = \sqrt{(2h)/g}, where h is the height and g is the acceleration due to gravity (9.8 m/s2). Substituting the given values:
t = \sqrt{(2*20m) / 9.8 m/s2} = \sqrt{(40 m) / 9.8 m/s2} = \sqrt{4.08 s2} = 2.02 s
The time in the air for the arrow is therefore approximately 2.02 seconds.
To calculate the horizontal range, we use the formula Range = velocity * time. Since the arrow is shot horizontally, its initial horizontal velocity is 40 m/s, and it maintains this speed because horizontal velocity is constant in the absence of air resistance:
Range = 40 m/s * 2.02 s = 80.8 m
The horizontal range of the arrow is therefore approximately 80.8 meters.