A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 24 seconds, and the average height of the bottle is 8 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. A cosine function can model the movement of the message in a bottle in relation to the height. Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. Part B: Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation? Part C: Based on the graph of the function, after how many seconds will it reach its lowest height?
A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 24 seconds, and the average height of the bottle is 8 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. A cosine function can model the movement of the message in a bottle in relation to the height.
Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t.
Part B: Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation?
Part C: Based on the graph of the function, after how many seconds will it reach its lowest height?
Given:
Time period between the maximum heights as 24 seconds.
Average height of the bottle is as 8 feet/
Bottle floating in the periodic manner.
Distance between the highest and the lowest point is 4 feet.
To find:
Model a cosine function for the bottle movement.
a) amplitude and period.
b) Equation of the function represents the situation.
c) Graph the function, find the seconds when it reaches the lowest height.
Concept used:
General equation of cosine:
Amplitude is defined as the distance of the maximum and minimum height divided by 2.
A period is defined as the distance between two maximum point or minimum point of the function.
The value is the phase shift from origin.
The value is the vertical shift.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
