Question
A theme park wants to make a new ride. The idea is that the ride rotates in a circular motion and sprays the riders every time they reach a certain height.
a) Choose values below that meet the conditions and then state them:
• 5, where 𝐿 is the lowest height of the ride (in metres)
• 50, where 𝑀 is the exact mid height of the ride (in metres)
• 20, where 𝑅 is the number of revolutions the ride makes in the
whole 5-minute ride time.
b) Create two equivalent sinusoidal equations, one using sine and the other
using cosine, representing the height, ℎ(𝑡), of the ride where 𝑡 represents
the time in seconds during the 5-minute ride time. Assume the ride starts at
the lowest height. Show all work to demonstrate how you obtained values
for both equations.
a) Choose values below that meet the conditions and then state them:
• 5, where 𝐿 is the lowest height of the ride (in metres)
• 50, where 𝑀 is the exact mid height of the ride (in metres)
• 20, where 𝑅 is the number of revolutions the ride makes in the
whole 5-minute ride time.
b) Create two equivalent sinusoidal equations, one using sine and the other
using cosine, representing the height, ℎ(𝑡), of the ride where 𝑡 represents
the time in seconds during the 5-minute ride time. Assume the ride starts at
the lowest height. Show all work to demonstrate how you obtained values
for both equations.
Answers
oobleck
f it starts at the lowest height, that means you want
h(t) = A - B cos(kt)
Now, using the given data. you have
frequency = 20/5, so period = 1/4. k = 4*360 = 1440
h(t) = 50 - (50-5) cos(1440t)
h(t) = A - B cos(kt)
Now, using the given data. you have
frequency = 20/5, so period = 1/4. k = 4*360 = 1440
h(t) = 50 - (50-5) cos(1440t)