The diameter of a car's tire is 52 cm. While the car is being driven, the tire picks up a nail. How high above the ground will the nail be after the car has travelled 0.1 km?
can someone please explain how to solve this question?
C = 3.14 * 52 cm = 163.4 cm/rev.
0.1 km = 100 m = 10000 cm.
10000 cm / 163.4 cm/rev - 61.2 REVs.
d = 0.2 rev * 163.4 cm/rev = 32.7 cm
above ground.
Thank youu !
yolo
How did you get 0.2 rev?
To solve this question, we need to make a few assumptions. First, we assume that the car's tire does not deflate due to the nail. Second, we assume that the nail remains in the same position relative to the ground as the tire rotates.
Here's how we can solve the question step by step:
1. Convert the distance traveled from kilometers to centimeters since the diameter of the tire is given in centimeters. There are 100,000 centimeters in 1 kilometer, so 0.1 km is equal to 10,000 cm.
2. Find the number of full rotations the tire makes. The distance traveled is equal to the circumference of the tire multiplied by the number of rotations. The circumference of a circle is calculated using the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 52 cm, so the circumference is 52π cm. Divide the total distance traveled (10,000 cm) by the circumference (52π cm) to find the number of rotations.
Number of rotations = 10,000 cm / (52π cm)
3. Multiply the number of rotations by the height the nail is sticking out from the ground for each full rotation. In this case, the height is equal to the diameter of the tire (52 cm).
Height above the ground = Number of rotations x Height per rotation
Height above the ground = (10,000 cm / (52π cm)) x 52 cm
4. Simplify the expression by canceling out the common units of cm.
Height above the ground ≈ (10,000 / (52π)) x 52 cm
Height above the ground ≈ (10,000 / π) cm
So, after the car has traveled 0.1 km, the nail will be approximately (10,000 / π) cm or approximately 3182.68 cm above the ground. Note that this calculation assumes the nail remains in the same position relative to the ground as the tire rotates.