Answer:
a) 35.2 m (1 d.p.)
b) 22 complete rotations
Step-by-step explanation:
Part a
One complete rotation of the big wheel of Freya's penny-farthing is equivalent to the length of the circumference of the wheel. Therefore, if the big wheel completes exactly 8 rotations, the distance Freya rode is equal to 8 times the circumference of the big wheel.
The formula for the circumference of a circle is C = πd, where d is the diameter. Given that the diameter of the big wheel is d = 1.4 m, then:
[tex]\textsf{Distance Freya rode}=8 \times \pi \times 1.4\\\\\textsf{Distance Freya rode}=11.2 \pi\\\\\textsf{Distance Freya rode}=35.18583772...\\\\\textsf{Distance Freya rode}=35.2\; \sf m\;(1\;d.p.)[/tex]
Therefore, the distance Freya rode was 35.2 m (rounded to one decimal place).
[tex]\dotfill[/tex]
Part b
To determine how many complete rotations the small wheel made while Freya was riding, we need to divide the circumference of the small wheel by the exact total distance Freya rode (from part a).
Given that the diameter of the small wheel is 0.5 meters, then its circumference is 0.5π meters. The exact distance Freya rode was 11.2π meters, so:
[tex]\textsf{Number of rotations}=\dfrac{\sf Total \;distance\;rode}{\textsf{Circumference of small wheel}}\\\\\\\textsf{Number of rotations}=\dfrac{11.2\pi}{0.5\pi}\\\\\\\textsf{Number of rotations}=\dfrac{11.2}{0.5}\\\\\\\textsf{Number of rotations}=22.4[/tex]
Therefore, the small wheel made 22.4 rotations, which means it made 22 complete rotations while Freya was riding.
