Question

Suppose that an artillery piece has a range R=1.512×10⁴ yards. Find its range in miles. Use the conversions 1mile=5280ft and 3ft=1yard. Express your answer to three significant figures in miles.

Answer 1

To find the range of an artillery piece in miles, we need to convert the given range from yards to feet and then from feet to miles using the given conversion factors. The range is approximately 8.59 miles.

Step-by-step explanation:

To find the range of an artillery piece in miles, we need to use the given conversion factors. The conversion factor given is 1 mile = 5280 feet and 3 feet = 1 yard. First, we need to convert the range from yards to feet by multiplying it by the conversion factor 3 feet = 1 yard. Then, we can convert the range from feet to miles by dividing it by the conversion factor 1 mile = 5280 feet. Finally, we round the answer to three significant figures.

Given that R = 1.512 × 10⁴ yards:

1. Convert yards to feet: 1.512 × 10⁴ yards * 3 feet/1 yard = 4.536 × 10⁴ feet.
2. Convert feet to miles: 4.536 × 10⁴ feet / 5280 feet/1 mile = 8.590 × 10⁻¹ miles.
3. Rounded to three significant figures: 8.59 miles.