Final answer:
Rachel's linear speed on the merry-go-round is approximately 6.28 feet per second and her angular speed is approximately 0.45 radians per second, after conversion from revolutions per second.
Step-by-step explanation:
To calculate Rachel's linear and angular speeds on the merry-go-round, we must first find the circumference using the provided diameter. The diameter is 14 feet, so the circumference (C) is C = πd, which is approximately 43.98 feet (π times 14 feet). Given that it takes 7 seconds for the merry-go-round to make a complete revolution, the linear speed (v) can be calculated as the circumference divided by the revolution time, so v = C / T, which equals about 6.28 feet per second, rounded to two decimal places.
The angular speed (ω) is the number of revolutions per second which is 1/7 rev/s, and this can be converted to radians per second by multiplying by 2π. So, ω = (1/7) / (2π), which equals approximately 0.45 radians per second, also rounded to two decimal places.