Final answer:
To calculate the time it takes for a rock to fall the first 50 meters from a 250-meter-high cliff, we use the kinematic formula, resulting in approximately 3.19 seconds for the rock to fall this distance.
Step-by-step explanation:
The question is about calculating the time it takes for a rock to fall the first 50 meters after being dropped from a 250-meter-high cliff. To solve this problem, we use the kinematic formula for free fall under the acceleration due to gravity. Assuming there is no air resistance, the time it takes to fall a certain distance can be calculated using the equation d = (1/2)gt^2, where d is the distance fallen, g is the acceleration due to gravity (approximately 9.81 m/s2), and t is the time in seconds. For the first 50 meters, we rearrange the formula to solve for t:
t = √(2d/g)
Using the given distance of 50 meters, we calculate:
t = √(2 * 50 m / 9.81 m/s2)
= √(100/9.81)
= √(10.1937)
≈ 3.19 seconds
Therefore, it takes approximately 3.19 seconds for the rock to fall the first 50 meters.