Question

A bullet leaving the muzzle of a pistol was traveling at a speed of 2230 feet per second. What is this speed in miles per hour?

Short answer

The speed of the bullet is approximately 1519.7 miles per hour.

Step-by-step solution

Understand the Conversion Factors

To convert feet per second to miles per hour, we need to know the conversion factors. There are 5280 feet in a mile and 3600 seconds in an hour.

Set Up the Conversion

We need to multiply the speed in feet per second by the conversion factor to get the speed in miles per hour. This can be achieved by multiplying by the number of feet in a mile (5280) and dividing by the number of seconds in an hour (3600).

Calculate the Speed in Miles per Hour

Now convert the speed of 2230 feet per second to miles per hour using the conversion factors. calculate: \(2230 \frac{feet}{second} \times \frac{1 mile}{5280 feet} \times \frac{3600 seconds}{1 hour} = 2230 \times \frac{1}{5280} \times 3600 \frac{miles}{hour}\).

Perform the Multiplication and Division

Perform the multiplication and division from the previous step to find the speed in miles per hour. calculate: \(2230 \times \frac{1}{5280} \times 3600 = 1519.7 \frac{miles}{hour}\) (rounded to one decimal place).

Key concepts

Conversion Factors

When working with different units in chemistry and physics, it's essential to use conversion factors to change one unit to another. A conversion factor is a fractional quantity that you use to multiply or divide a number, resulting in a unit change while maintaining its actual value.

For example, when you have a distance in feet but you need it in miles, or a time in seconds but require it in hours, you'll need the appropriate conversion factors to bridge the gap between these units. These factors are based on defined relationships between units, such as there being exactly 5280 feet in one mile or 3600 seconds in one hour. Using conversion factors entails creating a fraction that has the value of one, so it doesn't change the quantity's value, only the units.

In practice, you'll set up your calculation so that the unwanted units cancel out, leaving you with only the desired units. This process is often referred to as 'unit analysis' or 'dimensional analysis' and is a cornerstone of accurate and precise scientific measurements and calculations.

Feet to Miles Conversion

The process of converting feet to miles is a common task in many scientific calculations, such as determining the speed of an object in different units. To perform a feet to miles conversion, you need to use the conversion factor that equates feet and miles. Since 1 mile equals 5280 feet, the conversion factor from feet to miles is \( \frac{1 mile}{5280 feet} \).

To convert feet to miles, you multiply the number of feet by this conversion factor. The feet units will cancel each other out, and you're left with miles. For example, if you have 2230 feet and wanted to know how many miles that is, your calculation using the conversion factor would look like: \(2230 feet \times \frac{1 mile}{5280 feet} = 0.422 \text{ miles}\) (rounded to three decimal places).

Understanding this conversion is particularly vital when dealing with speeds, distances, and measurements that can vary greatly in magnitude and when it's more appropriate to express the quantity in larger or smaller unit increments.

Speed and Velocity

The concepts of speed and velocity are closely related but distinct in the world of physics. Speed is a scalar quantity which measures how fast an object is moving. It is the rate of change of distance with respect to time and does not concern the direction of movement. Conversely, velocity is a vector quantity that includes both the speed of an object and the direction of its motion.

When calculating speed, you'll often need to convert the units to match the context of the problem or to comply with standard units in physics, such as converting feet per second to miles per hour for ease of understanding or to align with other measurements. Speed is calculated by dividing the distance traveled by the time it takes to travel that distance. Using the correct conversion factors to adjust units is critical to ensure that the speed is accurately represented, whether it is in a scientific study or simply for practical information like determining how long it will take to travel a certain distance by car.