the diameter of a car tire is 52cm. While the car is being driven the tier picks up a nail how high above the ground will the nail be after the car has traveled 0.1km
the car travels .52π m per revolution
100 m / (.52π m/rev) = ? rev
the decimal portion of the revolutions gives the fraction of a turn where the nail is located
To determine how high above the ground the nail will be after the car has traveled 0.1 km, follow these steps:
Step 1: Convert 0.1 km to centimeters.
1 kilometer (km) = 100,000 centimeters (cm)
0.1 km = 0.1 * 100,000 cm
0.1 km = 10,000 cm
Step 2: Calculate the number of rotations made by the tire.
Since the diameter of the car tire is given as 52 cm, we can calculate the circumference of the tire using the formula: circumference = π * diameter.
Circumference = π * 52 cm
Circumference ≈ 3.14 * 52 cm
Circumference ≈ 163.28 cm
To find the number of rotations, divide the distance traveled by the circumference of the tire.
Number of rotations = Distance traveled / Circumference
Number of rotations = 10,000 cm / 163.28 cm ≈ 61.28 rotations
Step 3: Calculate the height the nail will be above the ground.
Since every rotation of the tire will result in the nail moving a distance equal to the circumference of the tire, we can multiply the number of rotations by the circumference to find the distance traveled by the nail.
Distance traveled by the nail = Number of rotations * Circumference
Distance traveled by the nail ≈ 61.28 rotations * 163.28 cm
Distance traveled by the nail ≈ 10,000.31 cm
So, the nail will be approximately 10,000.31 cm (or 100 meters) above the ground after the car has traveled 0.1 km.
To solve this problem, we need to understand some key relationships:
1. The diameter of the car tire is given as 52 cm. The diameter is the distance across the tire through its center.
2. The nail gets picked up by the tire while the car is being driven. As the tire rolls, the nail maintains its initial height above the ground.
3. The car travels a distance of 0.1 km, which is equivalent to 100 meters.
To find out how high above the ground the nail will be after the car has traveled 0.1 km, we need to determine how many times the tire rotates during this distance and then calculate the vertical distance the nail moves.
To calculate the number of tire rotations:
- First, find the circumference of the tire. The circumference is equal to the distance around the tire.
- The formula for circumference is: Circumference = π * Diameter.
- Substituting the given diameter value of 52 cm into the formula: Circumference = π * 52 cm.
To calculate the vertical distance the nail moves:
- The vertical distance will be equal to the circumference of the tire because the nail maintains its initial height above the ground.
- So, the vertical distance = Circumference.
Now, let's calculate the values:
Circumference = π * 52 cm.
Considering π (pi) as approximately 3.14, the circumference is:
Circumference = 3.14 * 52 cm.
Next, calculate the number of rotations in 0.1 km (100 meters):
- Divide the distance travelled (100 meters) by the tire's circumference to get an approximate number of rotations.
Number of rotations = 100 meters / Circumference.
Finally, calculate the vertical distance the nail moves:
- The vertical distance will be equal to the number of rotations multiplied by the circumference.
Vertical distance = Number of rotations * Circumference.
After calculating these values, you will have the height above the ground that the nail will be after the car has traveled 0.1 km.