A soccer ball of diameter 30 cm rolls without slipping at a linear speed of 3.1 m/s. Through how many revolutions has the soccer ball turned as it moves a linear distance of 15 m?

Well, let's calculate that using my amazing clown math skills!

First, we need to find the circumference of the soccer ball.

Circumference = π × Diameter

Circumference = 3.14 × 30 cm
Circumference = 94.2 cm

Now, we need to find out how many times the soccer ball's circumference fits into the linear distance it has moved.

15 m = 1500 cm

Number of revolutions = Linear distance / Circumference

Number of revolutions = 1500 cm / 94.2 cm
Number of revolutions ≈ 15.93

So, the soccer ball has turned approximately 15.93 revolutions. Just imagine all those fancy spins!

To find the number of revolutions the soccer ball has turned, we need to find the circumference of the ball and divide the linear distance traveled by it.

The circumference of a circle can be calculated using the formula:

C = π * d,

where C is the circumference and d is the diameter.

Given that the diameter of the soccer ball is 30 cm, we can calculate the circumference:

C = π * 30 cm = 30π cm.

But the linear distance is given in meters, so we need to convert the circumference to meters:

C = 30π cm * (1 m / 100 cm) = 0.3π m.

Now we can calculate the number of revolutions by dividing the linear distance traveled by the circumference:

Number of Revolutions = Linear Distance / Circumference.

Given that the linear distance is 15 m and the circumference is 0.3π m, we can calculate:

Number of Revolutions = 15 m / (0.3π m) = (50 / π) revolutions.

Thus, the soccer ball has turned approximately 15.915 revolutions.

To find the number of revolutions the soccer ball has turned, we need to know the relationship between linear distance, diameter, and revolutions.

One revolution is defined as a complete circular motion around the ball's circumference. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

We are given the diameter of the soccer ball, which is 30 cm or 0.3 m. Therefore, the circumference of the soccer ball is C = π * 0.3 = 0.942 m (approximately).

Now, we can find the number of revolutions using the formula:

Number of revolutions = Linear distance / Circumference

Plugging in the given values, we have:

Number of revolutions = 15 m / 0.942 m ≈ 15.91

So, the soccer ball has turned approximately 15.91 revolutions as it moves a linear distance of 15 m.