Final answer:
Given that the stone is thrown horizontally at 23 m/s from the top of a cliff 65 meters high, we want to determine how long it takes for the stone to reach the ground. Using the formula for vertical motion under gravity, the stone thrown horizontally from the cliff at 23 m/s is in the air for approximately 3.64 seconds.
Step-by-step explanation:
The student asks about the time a stone remains in the air when thrown horizontally from a cliff.
This is a physics problem that involves projectile motion.
The horizontal velocity is irrelevant to the time it takes to fall; only the vertical distance and the acceleration due to gravity (9.81 m/s2) are important for this calculation.
To find the time, we use the formula for the vertical motion of objects under gravity:
distance = 0.5 * g * t2
where g is the acceleration due to gravity and t is the time in seconds.
Arranging the formula to solve for t, we get:
t = sqrt((2 * distance) / g)
Plugging in the values, we get:
t = sqrt((2 * 65 m) / 9.81 m/s2)
t = sqrt(13.237 s2)
t ≈ 3.64 s
The stone is in the air for approximately 3.64 seconds, which when rounded to the nearest hundredth is 3.64 sec.