Practical_Antenna_Handbook_0071639586

A p p e n d i x A : U s e f u l M a t h 713
Suppose the sun is directly overhead at the time when you decide to go for a ride,
so that the shadow of the chair you’re riding in appears on the ground directly beneath
the Ferris wheel. Once your ride has begun, the Ferris wheel rotates at a constant speed,
passing the loading gate at the bottom once every 20 seconds, even though each time
you go over the top it feels as though you’re suddenly going faster.
Your friend, meanwhile, stands on the ground alongside the Ferris wheel, with an
extremely accurate clock. Eleven stripes of white paint appear on the ground alongside
the carnival ride, dividing the diameter of the wheel into 10 equal segments, as shown
in Fig. A.3.2. As you enjoy your ride, your friend marks down the exact time the shadow
from your chair passes over each stripe. Of course, every 20 seconds he notes that your
chair passes by the loading gate and 10 seconds later it is at the top of the arc, directly
above the loading gate.
While you’re staggering off the Ferris wheel at the end of your ride, your friend is
busy using his scientific calculator or an app on his smartphone to make a graph of the
position of your car’s shadow as a function of elapsed time. The graph he shows you
looks something like Fig. A.3.3, and if you connect the individual data points with a
PIVOT &
CHAIR MOUNT
CHAIR
LOADING GATE
PAINTED
STRIPES
x = –15'
Figure A.3.2 Ferris wheel test setup.
x = 0
x = +15'