Final answer:
To determine how long after reaching the low point a rider is 50 ft above the ground on a Ferris Wheel with a diameter of 50 ft and a center 30 ft above the ground, we can calculate the difference in height between the low point and the desired height, and then use the formula to calculate the time it takes for the rider to move that distance.
Step-by-step explanation:
To determine how long after reaching the low point a rider is 50 ft above the ground, we need to understand the motion of the Ferris Wheel. The Ferris Wheel makes one revolution every 40 seconds, which means it completes a full circle in that time. The diameter of the Ferris Wheel is 50 ft, so the radius is half of that, which is 25 ft.
When the rider is at the low point, they are 25 ft below the center of the wheel, which is 30 ft above the ground. So, the total height from the ground to the rider at the low point is 30 ft + 25 ft = 55 ft.
Now, we need to calculate how long it takes for the rider to reach a height of 50 ft above the ground. Since the rider starts at a height of 55 ft and goes up to 50 ft, the difference in height is 55 ft - 50 ft = 5 ft.
Since the Ferris Wheel completes one revolution every 40 seconds, we can calculate how long it takes for the rider to move 5 ft using the formula:
time = (distance / circumference) * one revolution time
time = (5 ft / (2π * 25 ft)) * 40 s
Using this equation, we can calculate that it takes approximately 5.1 seconds for the rider to be 50 ft above the ground after reaching the low point.