b.
76=40+60cos(PI/6 (t-2))
.6=cos(theta)
theta=arccos.6=.972 rad
.972=PI/6 (t-2)
solve for t.
c. evaluate dh/dt=-60*PI/6*sin(PI/6(t-2)
at the t in b. is it negative? then level is going down. Positive, increasing.
find times when h=0, then check between those times. your graph in a should help.
At a certain point on the beach, a post sticks out of the sand, its top being 76 cm above the beach. The depth of the water at the post varies sinusoidally with time due to the motion of the tides. The depth d is modeled by the equation d=40+60cos(pi/6(t-2)) where t is the time in hours since midnight.
a. Sketch a graph of the sinusoid curve without using a calculator
b. What is the earliest time of day at which the water level is just at the top of the post?
c. At the time you calculated in part b, is the post going under water or just emerging from the water? Explain
d. When d is negative, the tide is completely out and there is no water at the post. Between what times is the entire post out of the water?
1 answer
1 answer