1. A water wheel rung’s height as a function of time can be modeled by the equation: h - 8 = -9 sin6t
(b) Determine the maximum height above the water for a rung.

-1

Step-by-step explanation:

1. A water wheel rung’s height as a function of time can be modeled by the equation:

h - 8 = -9 sin6t

(b) Determine the maximum height above the water for a rung.

Given the rung's height modeled by the equation;

h - 8 = -9 sin6t

h(t) = -9sin6t + 8

At maximum height, the velocity of the rung is zero;

dh/dt = 0

dh/dt = -54cos6t

-54cos6t = 0

cos6t = 0/-54

cos6t = 0

6t = cos^-1(0)

6t = 90

t = 90/6

t= 15

Substitute t = 15 into the expression to get the maximum height;

Recall:

h(t) = -9sin6t + 8

h(15) = -9sin6(15) + 8

h(15) = -9sin90 + 8

h(15) = -9(1)+8

h(15) = -9+8

h(15) = -1

hence the maximum height above the water is -1