Pretest Answers

A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model h , the height in feet of the buoy in relation to sea level as a function of time, t , in seconds?

The height, h , in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t , in seconds can be modeled by the equation h is equal to 15 cosine open paren pi over 20 t close paren How long does it take for the waterwheel to complete one turn?

The height, h , in feet of a flag on one blade of a windmill as a function of time, t , in seconds can be modeled by the equation h is equal to 3 sine open paren 4 pi over 5 times open paren t minus 1 half close paren close paren plus 12 What is the minimum height of the flag?

Which of the following situations can be modeled with a periodic function?

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t is equal to 0 seconds. When the weight is released, it oscillates and returns to its original position at t is equal to 3 seconds. Which of the following equations models the distance, d , of the weight from its equilibrium after t seconds?

The height, h , in feet of the tip of the minute hand of a wall clock as a function of time, t , in minutes can be modeled by the equation h is equal to 0 point 7 5 cosine open paren pi over 30 times open paren t minus 15 close paren close paren plus 8 Which number (from 1 to 12 ) is the minute hand pointing to at t is equal to 0 ?

The displacement, d , in millimeters of a tuning fork as a function of time, t , in seconds can be modeled with the equation d is equal to 0 point 4 sine open paren 1760 pi t close paren What is the maximum displacement of the tuning fork?

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models d , the horizontal distance in inches of the pendulum from the center as a function of time, t , in seconds? Assume that right of center is a positive distance and left of center is a negative distance.

The height, h , in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t , in seconds can be modeled by the equation h is equal to 8 cosine open paren pi over 10 t close paren What is the period of the function?

The height, h , in feet of a ball suspended from a spring as a function of time, t , in seconds can be modeled by the equation h is equal to negative 2 sine open paren pi times open paren t plus 1 half close paren close paren plus 5 Which of the following equations can also model this situation?