The Tower of Terror is an elevator ride that has a 130 foot drop that is faster

Question

The Tower of Terror is an elevator ride that has a 130 foot drop that is faster than gravity. To prove this, many students put pennies on their knees at the start of the ride and watch the penny float in the air as the ride vehicle drops from an initial height of 180 feet above the ground at an initial velocity of -57.2 feet per second^2. The penny starts at the same initial height and the penny is falling at the acceleration due to gravity is about -32.2 feet per second^2. A. Find the position of the student as a function of time (t), and determine the position of the student after 2 seconds. B. Do the same for the penny. Find the position of the penny as a function of time (t), and determine the position of the penny after 2 seconds. C. What is the difference in the position of the penny and the student at t = 2 seconds?

Explanation / Answer

A) By second equation of motion,

delta h = 0.5 at^2

h = 180 + 0.5*-57.2 t^2

h = 180 - 28.6 t^2

when t=2 s

h = 65.6 feet above ground

B) h = 180 + 0.5*-32.2 t^2

h = 180 - 16.1t^2

After 2s, h = 180 - 16.1*4

= 115.6 ft

C) difference between position of penny and student

= 115.6-65.6

= 50 ft

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