when a vehicle is manufactured,its wheels are calibrated to rotate a specific number of times for given speeds with "standard" tires. Suppose a small pickup has standard tires with a radius of 14 inches. You decide to replace those tires with ones which have a radius of 16 inches. You are driving on the interstate highway, and your speedometer is registering 70 miles per hour,which is the speed limit. Give a written explanation of why (or why not) you could receive a speeding ticket. Include your calculations in your explanation.
Your true speed must be 70(16/14)
You figure out why. I will be happy to critique your solution.
an automobile is pushed so that its wheels turn three-quarters of a revolution. if the tires have a radius of 15 inches, how many inches does the car move?
To determine if you could receive a speeding ticket when replacing the tires on your small pickup, we need to consider how the change in tire radius affects the speedometer reading. The speedometer measures the rotational speed of the wheels and calculates the vehicle's speed based on the assumption that the wheels have a specific radius.
The number of rotations per minute (RPM) of the wheels is directly proportional to the vehicle's speed. When you increase the tire radius from 14 inches to 16 inches, the circumference of the tire increases because the circumference is directly related to the radius - it's approximately double the radius times pi (π).
First, we need to calculate the original circumference of the tire:
C1 = 2 * π * r1,
where r1 is the original tire radius of 14 inches.
C1 = 2 * 3.14159 * 14 = 87.96434 inches
Next, let's calculate the new circumference of the tire:
C2 = 2 * π * r2,
where r2 is the new tire radius of 16 inches.
C2 = 2 * 3.14159 * 16 = 100.53096 inches
Now, let's compare the two circumferences: C1 (original) and C2 (new).
Since the circumference of the larger-radius tire (C2) is greater than the circumference of the original tire (C1), it means that for every rotation of the wheel, the vehicle will travel a greater distance. Consequently, if you are driving using the same RPM as before, your vehicle will be moving faster than what is indicated on the speedometer.
To find out how much faster, we can calculate the ratio between the two circumferences:
Ratio = C2 / C1
Ratio = 100.53096 / 87.96434 = 1.142857
This ratio implies that the new tire will cover around 1.14 times the distance covered by the original tire for every rotation.
Considering that your speedometer is displaying 70 miles per hour (mph), this reading is based on the assumption of the original tire radius. However, since the new tire covers a greater distance for each rotation, your actual speed will be faster than what is shown on the speedometer.
To find the actual speed, multiply the displayed speed by the ratio:
Actual Speed = Displayed Speed * Ratio
Actual Speed = 70 mph * 1.142857 = 80 mph (approximately)
Therefore, when driving at a speedometer-displayed speed of 70 mph, your actual speed with the new tires would be about 80 mph. This exceeds the speed limit of 70 mph, so you could potentially receive a speeding ticket.
It's important to note that the calculation provided is a general approximation, and the actual difference in speed may vary due to factors like tire pressure, tire wear, and other variables. Additionally, different jurisdictions may have specific rules and regulations regarding speedometer accuracy and tire modifications, so it's always best to consult local laws and regulations.