A car's wheel (with tire) is 26 inches in diameter and its center is 12 inches above the road. If the car is traveling at 60 feet per second, how fast is the highest point of the tire moving relative to the ground?

The tire must be somewhat flat since the axle is not at the midpoint of the nominal diameter. It is 14 inches from the axle to the top of the tire. The speed of the top of the tire with respect to the axle will be 14/12 = 7/6 of the speed of the bottom of the tire, which is the car's speed.

(7/6) x 60 = 70 ft/s

Why did the tire go to school? Because it wanted to get a higher education!

Now, let's put our humorous hat aside and tackle your question. To find the speed of the highest point of the tire relative to the ground, we can use a little bit of math.

First, we need to convert the car's speed from feet per second to inches per second because the diameter of the tire is given in inches. There are 12 inches in a foot, so 60 feet per second would be 60 times 12 = 720 inches per second.

The highest point of the tire will move faster than the car's overall speed because it also has rotational motion. At the highest point, the tire is halfway up its rotation, meaning it has traveled half the circumference.

The circumference of the tire is calculated using the formula: circumference = π * diameter. Plugging in the diameter of 26 inches, we get: circumference = 3.14 * 26 = 81.64 inches.

Since the highest point of the tire has traveled half this distance, we divide the circumference by 2: 81.64 / 2 = 40.82 inches.

So, considering the tire's rotational motion, the highest point of the tire is moving 40.82 inches per revolution.

Since the tire makes one complete revolution as the car moves forward, the speed of the highest point of the tire relative to the ground is 40.82 inches per second.

To find the speed of the highest point of the tire relative to the ground, we can break down the problem into several steps:

Step 1: Convert the car's speed from feet per second to inches per second.
Since 1 foot is equal to 12 inches, we can convert the car's speed of 60 feet per second to inches per second by multiplying by 12:
60 feet/second * 12 inches/foot = 720 inches/second

Step 2: Determine the circumference of the wheel.
The circumference of a circle can be found using the formula C = π * d, where d is the diameter of the wheel. Given that the diameter is 26 inches, the circumference of the wheel is:
C = 3.14 * 26 inches = 81.64 inches

Step 3: Calculate the distance traveled by the highest point of the tire in one second.
Since the wheel rotates one full revolution for every revolution of the car, the distance traveled by the highest point of the tire in one second is equal to the circumference of the wheel.
Distance traveled by highest point in 1 second = Circumference of the wheel = 81.64 inches

Step 4: Determine the speed of the highest point of the tire relative to the ground.
The speed of the highest point of the tire relative to the ground is equal to the distance traveled divided by the time taken.
Speed = Distance traveled by highest point in 1 second / Time taken in 1 second
Speed = 81.64 inches / 1 second = 81.64 inches/second

Therefore, the highest point of the tire is moving at a speed of 81.64 inches per second relative to the ground.

To find the speed of the highest point of the tire relative to the ground, we can consider the rotational motion of the wheel.

First, let's convert the car's speed from feet per second to inches per second. Since 1 foot is equal to 12 inches, the car's speed is:

60 feet per second * 12 inches per foot = 720 inches per second

The diameter of the wheel is 26 inches, which means the radius is half of the diameter, so:

Radius = 26 inches / 2 = 13 inches

Now, we need to find the circumference of the wheel. Since the circumference is equal to 2 times pi times the radius, we have:

Circumference = 2 * 3.14 * 13 inches ≈ 81.64 inches

In one revolution of the wheel, the car will travel a distance equal to the circumference of the wheel. Therefore, the number of revolutions per second is:

Revolutions per second = car speed / circumference

Revolutions per second = 720 inches per second / 81.64 inches ≈ 8.82 revolutions per second

Since the highest point of the tire is located at the circumference of the wheel, the speed of the highest point of the tire relative to the ground is equal to the speed of the wheel's circumference. Thus, the highest point of the tire is moving at a speed of approximately:

Speed = Revolutions per second * circumference

Speed = 8.82 revolutions per second * 81.64 inches ≈ 720 inches per second

Therefore, the highest point of the tire is moving at a speed of approximately 720 inches per second relative to the ground.