.
A ride at an amusement park completes one rotation every 45s. The cars reach a maximum of 5m above the ground
and a minimum of 1m off the ground.
The height h in metres above the ground after t seconds can be represented using a sine or cosine function.
The ride begins at its minimum height.
a) Determine the equation that represents this function
b) How high above the ground is the ride at 100 seconds?
I have figured this out, the k value is360/45=8, the amp is 2 and the equation of the axis is 3.
the equation I figured out was h(t)=-2cos(8t)+3 and for b) I got the answer of 2.65m
Is this correct?
Thank you
~~~~~~~~~~~~~~~~~~~~~
You correctly determined the amplitude (2 meters) and the position of the axis = 3 meters.
You correctly use the cosine function, but you incorrectly determined its period.
The correct function is y =
Notice that in my function the period is exactly 45 seconds, as stated in the problem.
Do the rest using my function.
-----------------
Also, from my solution LEARN how to write a periodic trigonometric function, when the period is given in the problem.
If the period is T units of time and if there is no time shift (as in the given problem),
then the argument of the periodic harmonic function is , where t is the current time.