Final answer:
The potential energy of a 4 lb. book held 50 feet in the air is closest to 268 J when converting the weight to kilograms, the height to meters, and using the formula for gravitational potential energy with Earth's gravity.
Step-by-step explanation:
To calculate the potential energy (PE) of an object, you can use the formula PE = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m/s2), and h is the height in meters. First, we need to convert the weight from pounds to the SI unit of mass (kilograms), knowing that 1 lb is approximately 0.453592 kg. For a 4 lb. book, the mass would be 4 lb × 0.453592 kg/lb = 1.814368 kg.
Next, the height should be converted from feet to meters, where 1 foot is approximately 0.3048 meters. At 50 feet, the height in meters would be 50 ft × 0.3048 m/ft = 15.24 meters.
Now we can use the formula: PE = mgh = (1.814368 kg) × (9.8 m/s2) × (15.24 m) = 270.65 J (joules). However, as none of the provided options perfectly matches this result, and considering that in physics problems rounding is common, the closest numbered answer would be (b) 268 J.