Final answer:
After 3 minutes and 45 seconds, the rider on a Ferris wheel with a diameter of 120 feet and the lowest point being 10 feet off the ground will be at the highest point. Thus, the rider will be 130 feet off the ground.
Step-by-step explanation:
To determine how high off the ground the rider is after 3 minutes and 45 seconds, we first note that the Ferris wheel takes 180 seconds for one complete revolution (i.e., 3 minutes). Therefore, 3 minutes and 45 seconds is equivalent to 3 minutes plus 45 seconds, which is one full revolution plus one-quarter of another revolution.
Since the Ferris wheel's diameter is 120 feet, its radius is 60 feet. As the rider completes one full revolution and starts another, we look at the position after one-quarter of the next revolution. Since the direction of rotation is counter-clockwise, one-quarter rotation from the bottom will place the rider at the highest point of the Ferris wheel.
The highest point of the Ferris wheel is the diameter plus the height from the ground of the lowest point, which is 120 feet + 10 feet = 130 feet. Therefore, the rider will be 130 feet off the ground after 3 minutes and 45 seconds.