Final answer:
To calculate the height of the cliff from which a ball is dropped and takes 4.5 seconds to hit the ground, the equation for distance under constant acceleration (d = (1/2)gt²) is used with the given time t=4.5 seconds and gravity g=9.8 m/s², resulting in a height of approximately 99.225 meters.
Step-by-step explanation:
Calculating the Height of the Cliff
The question asks to calculate the height of a cliff when a ball dropped off it takes 4.5 seconds to hit the ground. To solve this problem, we can use the equation of motion under constant acceleration due to gravity. The equation to calculate the distance fallen is d = (1/2)gt², where d is the distance, g is the acceleration due to gravity (9.8 m/s² on Earth), and t is the time taken to fall.
Plugging the values we get: d = 1/2 × 9.8 m/s² × (4.5 s)². Calculating this gives us d = 1/2 × 9.8 m/s² × 20.25 s² = 99.225 m. So the height of the cliff is approximately 99.225 meters.