Question

At midnight the water at a particular beach is at high tide. At the same time a gauge at the end of a pier reads 10 feet. Low tide is reached at 6 AM when the gauge reads 4ft.


Answer the questions that follow using this scenario.


Determine the amplitude.

a.) 6 feet
b.) -3 feet
c.) 3 feet
d.) 12 feet

Only answer if you're smart, this question is worth 10 points :) thank you

Answer 1

The motion of tides can be roughly modelled using a sine function, i.e. asin(bx)+c

The amplitude of a sine graph is half the distance from the maximum to the minimum, so in this case it is (10-4)/2 = 3
Amplitudes are the equivalent of absolute values (i.e. think of it as the distance to a number on a number line, disregarding which way you're going), and therefore can only be positive. Therefore the amplitude of this is c) 3 feet, since at mid tide the buoy will be at 7 feet, climbing to 10 feet and falling to 4 feet, cyclically.