A bath toy is floating stationary in water such that half of the toy is above water and half of the toy is below the water. A kid pulls the toy 3.3 cm down into the water and then lets go. The toy then proceeds to bob up and down. It bobs up and down 18 times in a minute.
NOTE: Let up be positive and down be negative for this problem
(d) What is the equation that describes the position of the object at any given time?
(e) Where is the toy at time t = 7.92 second?
(f) Give meaning to your answer in part (e). Is the toy mostly above the water or below the water at this time. Explain with evidence how you know this.
(d) The equation that describes the position of the object at any given time is:
y(t) = 1.65 cos(6πt) - 1.65
where y(t) is the position of the toy at time t.
(e) To find where the toy is at time t = 7.92 seconds, we plug in t = 7.92 into the equation:
y(7.92) = 1.65 cos(6π(7.92)) - 1.65
y(7.92) = 1.65 cos(47.52π) - 1.65
y(7.92) = 1.65 cos(180°) - 1.65
y(7.92) = 1.65(1) - 1.65
y(7.92) = 0
Therefore, at t = 7.92 seconds, the toy is at its equilibrium position which is the waterline.
(f) The toy is mostly above the water at time t = 7.92 seconds. This can be inferred from the fact that the position of the toy at t = 7.92 seconds is 0, which indicates that the toy is at equilibrium, or at the waterline. Since the waterline is where half of the toy is above and half is below the water, we can conclude that the toy is mostly above the water at this time.