Question

От дома до магазина велосипедист доехал за 16 минут, при этом колесо велосипеда совершил 3000 оборотов. Диаметр колеса 80 см. С какой скоростью ехал велосипедист? Чему равно расстояние от дома до магазина?

Answer 1

Ответ:

Расстояние:15075м

Средняя скорость:56/5км час

Answer 2

Calculation of Speed:

To calculate the speed at which the cyclist was traveling, we need to determine the distance traveled and the time taken. We are given that the cyclist traveled from home to the store in 16 minutes and that the bicycle wheel made 3000 revolutions. The diameter of the wheel is 80 cm.

First, let's calculate the distance traveled by the cyclist. The distance traveled is equal to the circumference of the wheel multiplied by the number of revolutions. The formula for the circumference of a circle is C = π * d, where C is the circumference and d is the diameter.

Using the given diameter of 80 cm, we can calculate the circumference as follows:

C = π * d = 3.14 * 80 cm = 251.2 cm

Next, we need to convert the distance from centimeters to meters, as it is a more commonly used unit for speed. There are 100 centimeters in a meter, so the distance traveled is:

251.2 cm = 2.512 meters

Now, let's calculate the speed. Speed is defined as the distance traveled divided by the time taken. The time taken is given as 16 minutes, but we need to convert it to hours to match the unit of the speed. There are 60 minutes in an hour, so the time taken is:

16 minutes = 16/60 hours = 0.267 hours

Finally, we can calculate the speed:

Speed = Distance / Time = 2.512 meters / 0.267 hours ≈ 9.41 meters per hour

Therefore, the cyclist was traveling at a speed of approximately 9.41 meters per hour.

Calculation of Distance:

To calculate the distance from home to the store, we can use the formula for the circumference of a circle. The circumference is equal to the distance traveled by the cyclist, which we calculated earlier as 2.512 meters.

Using the formula C = π * d, where C is the circumference and d is the diameter, we can rearrange the formula to solve for the diameter:

d = C / π = 2.512 meters / 3.14 ≈ 0.799 meters

The diameter represents the distance from one side of the circle to the other, which is equal to twice the radius. Therefore, the radius is:

Radius = d / 2 = 0.799 meters / 2 = 0.3995 meters

The distance from home to the store is equal to the radius of the circle, as the cyclist traveled in a straight line. Therefore, the distance from home to the store is approximately 0.3995 meters.

Please note that the calculations provided are based on the given information and assumptions made.