a) Diameter of this Ferris wheel is double the amplitude d=67⋅2=134m
b)At t = 0 raider will be at height of 67sin[12(0+0.0223)]+70=67sin(0.2676)+70≈ 87.71598.
c)Since sin[12(t+0.0223)]≤1 The rider is 67⋅1+70=137m high off the ground if he is at the top of the wheel.
d)Rider will be at the bottom of the Ferris wheel when his height is minimal, when sin[12(t+0.0223)]=−1, when 12(t+0.0223)=3π/4+2π⋅k
(t+0.0223)=(3π/4+2π⋅k)/12
t=−0.0223+(3π/4+2π⋅k)/12=−0.0223+π/16+π/6⋅k
e)If t1 and t2 are to consecutive moments when the rider is in the same place
12(t2+0.0223)−12(t1+0.0223)=2π, t2−t1=2π/12=π/6
Answer: a) 134m, b)87.71598, c) 137m, d) t=−0.0223+π/16+π/6⋅k e)π/6 .
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