Final answer:
Using the equations for vertical motion and horizontal motion, we find that the height of the cliff would be 240.145 meters (not matching the given options), and the horizontal distance traveled by the ball is 210 meters.
Step-by-step explanation:
The student's question involves calculating the height of a cliff and the horizontal distance traveled by a ball that rolls off the cliff at a given speed, and after a certain time, hits the ground. To solve this problem, we can use the equations of motion under gravity for the vertical drop and constant velocity for the horizontal motion.
For the vertical motion, the equation h = 1/2 g t^2 where g is the acceleration due to gravity (9.81 m/s2) and t is the time taken to hit the ground. Given that the time taken is 7 seconds, we find the height h as follows: h = 1/2 * 9.81 m/s2 * (7 s)2 = 240.145 m. Since none of the provided options match this value, it appears there may be a mistake in the given options or the question itself.
For the horizontal motion, we have a constant velocity of 30 m/s for 7 seconds, so the horizontal distance d = velocity * time = 30 m/s * 7 s = 210 meters, which matches option b) from the provided list.