Final answer:
The horizontal distance traveled by an arrow fired horizontally off a 12.0-meter cliff with a velocity of 55.5 m/s is approximately 86.6 meters.
Step-by-step explanation:
The question involves calculating the horizontal distance traveled by an arrow fired directly horizontal off a cliff that is 12.0 meters tall with a velocity of 55.5 m/s. This is a classic problem in physics dealing with projectile motion, where the only acceleration acting on the arrow is due to gravity (9.81 m/s2).
To find the time it takes for the arrow to hit the ground, we use the equation for vertical motion under constant acceleration:
d = vit + (1/2)at2
Since the initial vertical velocity (vi) is zero for horizontal launch, the equation reduces to:
12.0 m = (1/2)(9.81 m/s2)t2
Solving for t gives us approximately 1.56 seconds. We then calculate the horizontal distance traveled using the horizontal velocity:
distance = velocity x time
distance = 55.5 m/s x 1.56 s
The horizontal distance traveled by the arrow is therefore approximately 86.6 meters.