precal modeling changing amplitude

Question

A wheel with radius 22 cm is being pushed up a ramp at a rate of 88 cm per second. The ramp is 780780 cm long, and 120120 cm tall at the end. A point PP is marked on the circle as shown (picture is not to scale).

I don;t know how to find equation for hdight hp of the point p above the ground as function of t time in seconds

my euqation is

2\cos \left(2t\right)+2+\frac{48}{39}t

Answer 1

It looks to me as if the equation you have is height as a function of time. Looks like it is:

2cos(2t) + 2 + (48/39)t

However this is merely an expression the way it is written instead of a function. I would be guessing about what your expression is equal to (perhaps the height of the point p)

So maybe it is h(t) = 2cos(2t) + 2 + (48/39)t where h(t) is the height of point p at any time "t".

If so, use the length of the ramp and the speed to find the time, and just plug it into the function.

t = distance/rate

However, there seems to be more than this going on because the graph of what you have given looks like this:

And at t = 0 this function shows a height of about 4 and immediately turning down which would not match your radius of 22 cm. I suggest you re-submit the question with a correct function including stating what the variables are.