The diameter of a car's tire is 60cm . While the car is being driven , the tire picks up a nail .How high above the ground is the nail after the car has travelled 1km

vey similar to the ferris wheel problem I just did for you except this time the nail is at h = .30 - .30 cos 2 pi t/T

because it is at the bottom when t = 0

Jennifer drives 16 miles . She drives home along the same rout . How far does Jennifer drives?

A street that is 164m long is covered in snow. City workers are using a snowplow to clear the street. The snowplow has tires that are 1.5m in diameter. How many times does a tire have to turn in traveling the length of the street?

To find the answer, we need to determine how many times the tire rotates while the car has traveled 1 km and then calculate the height based on the diameter of the tire.

First, let's find out how many times the tire rotates while the car has traveled 1 km:

1 kilometer is equal to 1000 meters.
The circumference of a circle is calculated using the formula: circumference = 2 * pi * radius.

Given that the tire's diameter is 60 cm, the radius (r) will be half of the diameter, which is 30 cm or 0.3 meters (since 1 meter = 100 cm).
The circumference (C) of the tire will be 2 * pi * 0.3 = 1.88496 meters.

To find the number of rotations (N) needed to travel 1 km, we divide the distance traveled (1 km or 1000 meters) by the circumference of the tire:
N = 1000 meters / 1.88496 meters per rotation = 530.14 rotations (approx).

Since the nail is attached to the tire, it will rotate as well. Therefore, the nail will also make 530.14 rotations.

Now, to find the height above the ground, we can use the formula:

Height = Number of rotations * circumference

Height = 530.14 rotations * 1.88496 meters

Calculating this, we find that the height of the nail above the ground after the car has traveled 1 km is approximately 1000.44 meters.