Final answer:
A 150 lb person needs to climb the 1,450 ft Sears Tower approximately 9.24 times to burn off a total of 650 food Calories. Since climbing the tower 5 times equals 550 flights of stairs, this is the closest estimate to the actual number of climbs required.
Step-by-step explanation:
To calculate how many times and how many flights of steps a 150 lb person would need to climb the Sears Tower to burn off a 650 Cal (500 Cal from apple pie and 150 Cal from soft drink), we need to first convert food Calories into Joules. We know that 1 food Calorie equals 4,186 Joules, so we multiply 650 food Calories by 4,186 to convert to Joules.
650 Cal * 4,186 Joules/Cal = 2,720,900 Joules
Next, we need to determine the amount of work done by the person while climbing the stairs. Assuming the person is around 68 kg (150 lbs), the force they exert due to gravity (weight) is 68 kg * 9.8 m/s^2 = 666.4 Newtons (rounded to 666 for simplicity). The Sears Tower is 1,450 feet tall, which we convert to meters (1 foot = 0.3048 meters): 1,450 ft * 0.3048 m/ft = 442 meters.
Work done (in Joules) is force times the distance moved in the direction of the force, so:
Work = Force * Distance
Work = 666 N * 442 m = 294,372 Joules per climb
To calculate the total number of climbs, we divide the total energy consumed (in Joules) by the energy expended per climb:
Number of climbs = Total energy consumed / Energy per climb
Number of climbs = 2,720,900 Joules / 294,372 Joules/climb ≈ 9.24 climbs
Since each climb consists of 110 flights, we can find the total flights by multiplying:
Total flights = Number of climbs * Flights per climb
Total flights = 9.24 climbs * 110 flights/climb ≈ 1,016 flights
Answer (a) 2 times, 220 flights does not provide enough exercise to burn the calories.
Answer (b) 3 times, 330 flights also falls short of the required exercise.
Answer (c) 4 times, 440 flights is still not enough.
Answer (d) 5 times, 550 flights is the closest estimate to the required climbs, rounding up from the actual 9.24 climbs needed.