Let's solve the problem step by step.

Given data:

• The big wheel has a radius of 1.4 m.
• The big wheel makes 8 complete rotations.

(a) How far did Freya ride?

The distance traveled by the penny-farthing is equal to the circumference of the big wheel multiplied by the number of rotations.

1. Circumference of the big wheel: $C = 2\pi r = 2\pi (1.4) = 2.8\pi$ Approximating with $\pi \approx 3.1416$:

   $C \approx 2.8 \times 3.1416 = 8.7965 \text{ m}$

2. Total distance traveled: $D = 8 \times C = 8 \times 8.7965 = 70.4 \text{ m}$

   Final answer: 70.4 m (1 d.p.)

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

Since the small wheel covers the same total distance, we first need its radius (or diameter), which is not given in the image. However, we can assume that the missing measurement is its radius, and let's call it $r_s$.

If the small wheel’s radius were given, we would calculate its circumference:

$C_s = 2\pi r_s$

Then, the number of rotations the small wheel makes is:

$N_s = \frac{D}{C_s}$

If you can find the small wheel's radius or diameter, let me know so we can finish part (b) accurately.

Do you want more details or have any questions?

Related Questions:

1. What if the big wheel had a radius of 1.6 m instead of 1.4 m? How far would Freya ride?
2. If the small wheel had a radius of 0.3 m, how many rotations would it make?
3. How would the total distance change if the big wheel made 10 rotations instead of 8?
4. What is the relationship between wheel size and the number of rotations needed to cover a fixed distance?
5. How does changing the wheel radius affect the circumference of a circle?

Tip: The circumference of a circle is directly proportional to its radius, meaning doubling the radius doubles the distance traveled per rotation!