Question

A new roller coaster lets you get on at 60 feet high. Then you climb to 100 feet and go back down to 60 and lower to 20 feet before returning to 60 feet 15 seconds later. It repeats this pattern numerous times.

a) Find the amplitude.
b) Find the vertical shift.
c) Determine the period.
d) Calculate the frequency.
e) Find the height of the rider off the ground after 36 seconds

Answer 1

The amplitude is 100 feet, the vertical shift is 60 feet, the period is 15 seconds, the frequency is 0.067 Hz, and the height of the rider off the ground after 36 seconds is 60 feet.

Step-by-step explanation:

• a) The amplitude of the roller coaster's motion is the maximum height reached, which is 100 feet. So, the amplitude is 100 feet.
• b) The vertical shift is the average height of the oscillation, which is 60 feet. So, the vertical shift is 60 feet.
• c) The period of the roller coaster's motion is the time it takes to complete one full cycle. In this case, it is the time it takes to go from 60 feet to 100 feet and back to 60 feet. Since it takes 15 seconds to complete this cycle, the period is 15 seconds.
• d) The frequency of the roller coaster's motion is the number of cycles completed per second. It is the inverse of the period, so the frequency is 1/15 or 0.067 Hz.
• e) To find the height of the rider off the ground after 36 seconds, we need to determine how many complete cycles the roller coaster goes through in that time. Since the period is 15 seconds, the roller coaster completes 36/15 or 2.4 cycles in 36 seconds. Since each cycle starts and ends at 60 feet, the height of the rider off the ground after 36 seconds is also 60 feet.