Word problem time and height

Question

x f(x)

0 0.55

25 0.325

50 0.1

75 0.325

100 0.55

125 0.325

150 0.1

175 0.325

200 0.55

y=0.225 sin(π/50(x-75))+ 0.325

y= 0.255 cos(π/50(x))+0.325

How would you solve how much time in the first minute is the valve of the tire above 15 m

x=time (seconds) f(x)= height (meters) (height measured from the tip of the valve of the bicycle wheel all the way to the ground)

Answer 1

There is something wrong about the stated height: The function is never any where near 15 meters. Maybe, it's cm and you are looking for y = .15 m. Anyway,...

I would find the x values in the interval 0 to 60 seconds in which x* leads to this y* height specified. Let's say this happens at x1 and x2 only. In that case x2-x1 is the time spent over that height because you start below the height. If there are n sets of x1 and x2, the tmie above will be n(x2-x1) and, if there is no matching x2 at the end, then the time will be n(x2-x1) + 60- x*.

Good luck.