Final answer:
The ball will have fallen 35.91 meters after 2.7 seconds of free fall from a cliff, using the formula for vertical displacement in free fall. This calculation uses only the vertical motion, unaffected by the initial horizontal velocity.
Step-by-step explanation:
The question asks us to calculate how far down a ball has fallen after being thrown horizontally from a cliff, which is a problem of projectile motion in physics. Since the horizontal velocity does not affect vertical motion, we can use the equations of motion for free fall to solve it. The formula for the distance fallen under gravity is given by:
d = (gt^2) / 2
where g is the acceleration due to gravity (9.8 m/s^2) and t is the time the object has been falling. For our problem:
- g = 9.8 m/s^2
- t = 2.7 seconds
Now substitute the values into the formula:
d = (9.8 m/s^2 * (2.7 s)^2) / 2
After calculating, the ball will have fallen approximately 35.91 meters after 2.7 seconds. Since this distance is not in the options provided, it's possible there might be an error in the question or the listed options.