Final answer:
Using the principles of projectile motion in physics, the time for the rock to fall 60 meters is calculated, and this time is used to determine the horizontal distance traveled, which is 90 meters.
Step-by-step explanation:
The question concerns projectile motion, a topic in physics where an object is thrown near the Earth's surface and moves along a curved path under the action of gravity only.
Given that a rock is thrown horizontally with an initial velocity of 12 m/s from a height of 60 meters, we can determine how far from the base of the cliff the rock will land. To find out the horizontal distance, we need to calculate the time it takes for the rock to hit the ground and then use this time to calculate the horizontal distance traveled.
The time 't' to fall 60 meters can be found using the equation for vertical motion:
t = √(2h/g)
,
where 'h' is the height of 60 meters and 'g' is the acceleration due to gravity (approximately 9.8 m/s²). After finding 't', we can use the equation for horizontal motion:
d = vt
,
where 'd' is the horizontal distance, 'v' is the initial horizontal velocity (12 m/s), and 't' is the time calculated from the first step.
Using these steps, we can determine that the correct answer is (C) 90 meters.