Question

Сівши у кабінку атракціону «Колесо огляду», Василь визначив що колесо зробило один повний оберт за 5хв. Потім він з'ясував у працівника парку що радіус колеса 15м. Обчисліть швидкість руху кабінки та шлях що проходить кабінка за 10 годин роботи атракціону.

Answer 1

Calculation of the Speed of the Cabin

To calculate the speed of the cabin, we can use the formula:

Speed = Distance / Time

Given that the radius of the wheel is 15m and it completes one full rotation in 5 minutes, we can calculate the circumference of the wheel using the formula:

Circumference = 2 * π * Radius

Substituting the value of the radius (15m) into the formula, we get:

Circumference = 2 * π * 15m

Now, we can calculate the distance traveled by the cabin in one rotation:

Distance = Circumference

Next, we need to convert the time taken for one rotation from minutes to hours:

Time = 5 minutes = 5/60 hours

Finally, we can calculate the speed of the cabin:

Speed = Distance / Time

Let's calculate the values step by step.

Calculation Steps:

1. Calculate the circumference of the wheel: - Circumference = 2 * π * 15m - Circumference = 30π m

2. Calculate the distance traveled by the cabin in one rotation: - Distance = Circumference - Distance = 30π m

3. Convert the time taken for one rotation from minutes to hours: - Time = 5 minutes = 5/60 hours - Time = 1/12 hours

4. Calculate the speed of the cabin: - Speed = Distance / Time - Speed = (30π m) / (1/12 hours) - Speed = 360π m/h

Calculation of the Distance Traveled by the Cabin in 10 Hours

To calculate the distance traveled by the cabin in 10 hours, we can use the formula:

Distance = Speed * Time

Given that the speed of the cabin is 360π m/h and the time is 10 hours, we can calculate the distance traveled:

Distance = Speed * Time

Let's calculate the value.

Calculation Steps:

1. Calculate the distance traveled by the cabin in 10 hours: - Distance = Speed * Time - Distance = (360π m/h) * 10 hours - Distance = 3600π m

Therefore, the speed of the cabin is 360π m/h and the distance traveled by the cabin in 10 hours is 3600π m.

Please note that the values of π and m are constants, so the speed and distance are approximate values.