A passenger seated on a Ferris wheel is at a height (in meters) given by h(t)=60+50 (…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A passenger seated on a Ferris wheel is at a height (in meters) given by
h(t)=60+50sin(15πt),
where t is the time in seconds after the wheel begins turning.
(a) Determine the passenger’s average vertical velocity over the interval [10,12]. Give exact values of any trigonometric expressions and express the final answer to two decimal places with units.
(b) Determine the average vertical velocity over the shorter interval [10,10.1]. Express the result to two decimal places with units.
(c) Compare your answers from parts (a) and (b). Explain what the comparison suggests about the passenger’s instantaneous vertical velocity at t=10 seconds.
(d) At approximately what time in the next 15 seconds after t=10 would you expect the average vertical velocity over a short interval of length 0.1 second to be zero? Support your prediction with reasoning based on the structure of h(t).