Lee is running around the perimeter of a circular track at a rate of 10 ft/sec. The track has a radius of 100 yards. After 10 seconds, Lee turns and runs along a radial line to the center of the circle. Once he reaches the center, he turns and runs along a radial line to his starting point on the perimeter. Assume Lee does not slow down when he makes these two turns. How far has he travelled once he returns to his starting position?
Question is easier than it seems.
The only tricky part is to find the distance he covers around the circle in the first 10 seconds, and that will be measured in feet, while the distance to the centre is measured in yards.
So Lee runs for 10 seconds at 10 ft/s, then 100 yards, and then another 100 yards
= 100 + 300 + 300 feet = 700 feet
^ 700 is right idiot...
To find out how far Lee has traveled, we need to analyze his movements step by step.
Step 1: Calculate the distance traveled around the perimeter of the circular track in 10 seconds.
Since Lee is running at a rate of 10 ft/sec, in 10 seconds he will cover a distance of 10 ft/sec * 10 sec = 100 feet.
Step 2: Calculate the distance Lee travels along the radial line from the perimeter to the center of the circle.
The distance from the perimeter to the center of the circle is the radius of the circle, which is given as 100 yards. However, since we measured the distance traveled around the perimeter in feet, we need to convert 100 yards to feet:
100 yards * 3 feet/yard = 300 feet.
Step 3: Calculate the distance Lee travels along the radial line from the center back to his starting position on the perimeter.
Since Lee is now at the center of the circle, he needs to travel the radius of the circle (100 yards or 300 feet) back to his starting position on the perimeter.
Step 4: Add all the distances together to find the total distance Lee has traveled.
Total distance = Distance traveled around the perimeter + Distance from perimeter to center + Distance from center back to starting position
Total distance = 100 feet + 300 feet + 300 feet
Total distance = 700 feet.
Therefore, Lee has traveled a total distance of 700 feet once he returns to his starting position.