Final answer:
Using the principles of projectile motion, we find that the horizontal displacement of a cannonball launched from a 154 m high cliff with an initial speed of 31.7 m/s is approximately 177.52 meters.
Step-by-step explanation:
The question involves a cannonball launched horizontally from a cliff and requires us to determine the horizontal displacement of the cannonball. To solve this, we use the principles of projectile motion. Since the motion in the horizontal direction is at a constant velocity (because air resistance is ignored), and the only acceleration is due to gravity in the vertical direction, we can calculate the time it takes for the cannonball to hit the ground and then use that time to find out how far it traveled horizontally.
To find the time to hit the ground, we use the formula for the vertical motion:
distance = 0.5 × gravity × time², where gravity is 9.8 m/s². So, 154 m = 0.5 × 9.8 m/s² × time². Solving for time, we get that time is approximately 5.6 seconds. Now that we have the time, we can calculate the horizontal displacement using the formula:
displacement = velocity × time, where the velocity is given as 31.7 m/s. Therefore, displacement = 31.7 m/s × 5.6 s, which equals about 177.52 meters.
The horizontal displacement of the cannonball is 177.52 meters.