Question

1. Длина обода велосипеда состовляет l = 2м. Велосипедист проехал путь равный s= 2км 800м. Сколько оборотов вокруг своей оси при этом совершило колесо?

Answer 1

1400 метров за весь путь

Answer 2

Calculation of Wheel Revolutions

To calculate the number of wheel revolutions, we need to find the circumference of the wheel and divide the total distance traveled by the circumference.

Given: - Length of the wheel rim (circumference): l = 2m - Distance traveled by the cyclist: s = 2km 800m

To find the circumference of the wheel, we can use the formula:

Circumference = 2πr

However, we are not given the radius of the wheel, so we need to find it first.

Finding the Radius of the Wheel

To find the radius, we can use the formula:

Circumference = 2πr

Rearranging the formula, we have:

r = Circumference / (2π)

Substituting the given value of the circumference, we get:

r = 2m / (2π)

Simplifying the expression, we find:

r = 1 / π

Now that we have the radius, we can calculate the circumference of the wheel.

Calculating the Wheel Circumference

Using the formula for the circumference of a circle, we have:

Circumference = 2πr

Substituting the value of the radius, we get:

Circumference = 2π * (1 / π)

Simplifying the expression, we find:

Circumference = 2

Therefore, the circumference of the wheel is 2 meters.

Calculating the Number of Wheel Revolutions

To calculate the number of wheel revolutions, we divide the total distance traveled by the circumference of the wheel.

Given: - Distance traveled by the cyclist: s = 2km 800m - Circumference of the wheel: Circumference = 2m

To find the number of wheel revolutions, we use the formula:

Number of Wheel Revolutions = Distance Traveled / Circumference

Substituting the given values, we get:

Number of Wheel Revolutions = 2km 800m / 2m

Converting the distance to meters, we have:

Number of Wheel Revolutions = 2800m / 2m

Simplifying the expression, we find:

Number of Wheel Revolutions = 1400

Therefore, the wheel made 1400 revolutions around its axis during the cyclist's journey.