Let's break down the two questions in the image:

Part (a) – How far did Freya ride?

The large wheel has a radius of 1.4 meters, and it completes 8 complete rotations. The distance traveled in one complete rotation is the circumference of the large wheel.

The formula for the circumference of a circle is:

$C = 2 \pi r$

Where $r$ is the radius. For the large wheel:

$C = 2 \pi (1.4) = 8.796 \text{ meters (approximately)}$

Now, since the big wheel completes 8 rotations, the total distance Freya traveled is:

$\text{Distance} = 8 \times 8.796 = 70.368 \text{ meters}$

Rounding to one decimal place:

$\text{Distance} = 70.4 \text{ meters}$

So, Freya rode 70.4 meters.

Part (b) – How many complete rotations did the small wheel make?

The small wheel has a radius of 0.5 meters. The circumference of the small wheel is:

$C_{\text{small}} = 2 \pi (0.5) = 3.1416 \text{ meters}$

Since Freya rode a total of 70.4 meters, the number of rotations made by the small wheel can be found by dividing the total distance traveled by the circumference of the small wheel:

$\text{Number of rotations} = \frac{70.4}{3.1416} \approx 22.4$

Thus, the small wheel made approximately 22 complete rotations.

Let me know if you would like any further details or clarification!

Here are some additional questions you might find useful:

1. How would the distance change if the radius of the large wheel were doubled?
2. How could you calculate the number of rotations for a larger or smaller wheel?
3. What other methods could be used to solve this problem if we didn't know the radii?
4. How would the distance traveled change if Freya completed more rotations?
5. Could the distance be calculated without knowing the number of rotations of the large wheel?

Tip: To simplify solving circular motion problems like this, always start by calculating the circumference (distance per rotation) before moving to the next step.