The person's speed is approximately 8.7 m/s, calculated using the centripetal force formula and the tension in the cable, given the cable angle θ of 62° below the horizontal.
In this scenario, the person sitting in the chair is moving in a horizontal circle, and the task is to determine their speed. The situation involves a cable of length 6.0 m, and the cable makes an angle θ of 62° below the horizontal. The combined mass of the person and the chair is given as 80 kg.
The key to solving this problem lies in recognizing the tension in the cable as the centripetal force acting on the person. Using trigonometric relationships, the vertical component of the tension is equal to the gravitational force acting on the person, while the horizontal component provides the centripetal force required for circular motion.
By applying Newton's second law in both the vertical and horizontal directions and employing the centripetal force formula, the speed of the person can be determined. The calculated speed is approximately 8.7 m/s, reflecting the balance between gravitational and centripetal forces in the circular motion scenario.