Question

a care has wheels of radius 16 inches. the wheels are spinning at 800 rotations per minute. what is the speed of the vehicle in miles per hour

Answer 1

To find the speed of the car in miles per hour, calculate the circumference of the wheel using the radius, find the distance the car travels in one minute, and convert that to miles per hour resulting in a speed of approximately 76.4 MPH.

Step-by-step explanation:

To calculate the speed of the vehicle in miles per hour when the car's wheels of radius 16 inches are spinning at 800 rotations per minute (RPM), we first need to find out the circumference of a wheel, which is the distance that the car travels in one rotation of the wheel.

The circumference (C) is given by the formula:

C = 2πr

Where:

• π is Pi, approximately 3.14159
• r is the radius of the wheel

First, let's convert the radius to feet (as there are 12 inches in a foot) for convenience:

r = 16 inches × (1 foot / 12 inches) = 1.333 feet

Now, let's calculate the circumference:

C = 2π × 1.333 feet ≈ 8.38 feet

The car travels the distance of the circumference with each wheel rotation. To find the distance traveled in one minute, we multiply the circumference by the rate of rotation:

Distance per minute = 800 RPM × 8.38 feet

Distance per minute = 6704 feet/minute

There are 5280 feet in a mile, so to convert feet per minute to miles per hour, we use the following conversion:

Distance per hour = (Distance per minute × 60 minutes) / 5280 feet

Distance per hour = (6704 × 60) / 5280

Distance per hour = 76.3636 miles per hour (£MPH)

Answer 2

8.98 miles/hour

Step-by-step explanation:

To find the speed of the vehicle in miles per hour, you can first convert the number of rotations per minute to the number of rotations per hour by multiplying it by 60. So, the number of rotations per hour is 800 rotations/minute * 60 minutes/hour = <<800*60=48000>>48000 rotations/hour.

Then, you can use the formula for the circumference of a circle to find the distance traveled by one of the wheels in one rotation: C = 2 * pi * r, where C is the circumference, pi is approximately 3.14, and r is the radius of the wheel. So, the circumference of each wheel is 2 * 3.14 * 16 inches = <<23.1416=100.48>>100.48 inches.

Then, you can use the formula for speed: distance traveled / time traveled. Since the distance traveled by one of the wheels in one rotation is 100.48 inches, and there are 48000 rotations per hour, the distance traveled by one of the wheels in one hour is 48000 rotations/hour * 100.48 inches/rotation = 4.81E5 inches.

To convert this distance to miles, you can divide it by the number of inches per mile: 4.81E5 inches / (12 inches/foot * 5280 feet/mile) = 8.98 miles/hour. This is the speed of the vehicle.