Final answer:
To clear the rocks extending 3 meters beyond a 15-meter high cliff, the minimum horizontal velocity necessary for a cliff jumper is 1.71 m/s, calculated using the time of fall derived from projectile motion equations.
Step-by-step explanation:
The student is asking for the minimum horizontal velocity required for a cliff jumper to clear the rocks that extend 3.0 meters past the bottom of a 15-meter high cliff. To solve this problem, we need to use the physics of falling objects and projectile motion.
When the jumper runs off the cliff, gravity will pull them down at an acceleration of 9.81 m/s2. The time it takes to fall 15 meters can be found using the formula for the distance fallen under constant acceleration, which is d = 0.5 * g * t2, where d is the distance, g is the acceleration due to gravity, and t is the time. Solving for t, we find that the time of fall is approximately 1.75 seconds.
The minimum horizontal velocity (vh) needed to clear the rocks can then be found by dividing the horizontal distance to clear the rocks by the time of fall, which yields vh = distance/time. Hence, the minimum horizontal velocity for the cliff jumper to clear the rocks is 1.71 m/s (3.0 meters / 1.75 seconds).