Question

Suppose that the H of a Ferris wheel can be modeled by the function H(t)= -16cos(3.14t/45)+24, where t is the time in seconds. What is the maximum height of the cabin?

Answer 1

8feet

Explanation:

Given the height of the cabin modeled by the equation;

H(t)= -16cos(3.14t/45)+24

at the maximum height dH/dt = 0

dH/dt = 3.14/45(16)sin(3.14t/45)

dH/dt = 1.116sin(3.14t/45)

0 = 1.16sin(3.14t/45)

sin3.14t/45 = 0/1.16

sin3.14t/45 =0

3.14t/45 = arcsin0

3.14t/45 = 0

3.14t = 0

t = 0seccs

Substitute t = 0 into the expression

H(t)= -16cos(3.14t/45)+24

H(0) = -16cos(3.14(0)/45)+24

H(0) = -16cos0 + 24

H(0) = -16+24

H(0) = 8feet

Hence the maximum height of the cabin is 8feet