Pre-Cal 40S Slides March 12, 2008

The Mathematics of Tidal Waves

Giant waves on the seafront at Seaham, County Durham by freefotouk

At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given by this formula:

(a) State the: (i) period (ii) amplitude (iii) phase shift.

At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given by this formula:

(b) What is the maximum depth of the water? When does it occur?

At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given by this formula:

(c) Determine the depth of the water at 5:00 am and at 12:00 noon.

(d) Determine one time when the water is 2.25 meters deep.

At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given by this formula:

(d) Determine one time when the water is 2.25 meters deep.

Transformations Pre-Test

Quowned By The Cal

(b) Write a sine and a cosine equation for this function.

(c) Find one time when the point A is 4 meters above the water.

(b) Write a sine and a cosine equation for this function.

(c) Find one time when the point A is 4 meters above the water.

(d) For how long, during each revolution, is the point A within 4 meters of the water's surface?

A Ferris whell has a radius of 20 m. It rotates once every 40 seceonds. Passengers get on at point S, which is 1 m above ground level. Suppose you get on at S and the wheel starts to rotate.

(a) Graph how your height above the ground varies during the first two cycles.

(b) Write an equation that expresses your height as a function of the elapsed time.

(c) Determine your height above the ground after 45 seconds.

(d) Determine one time when your height is 35 m above the ground.

JAMIEELVEN

KRISTINA

This equation gives the depth of the water, h meters, at an ocean port at any time, t hours, during a certain day.

(a) Explain the significance of each number in the equation:(i) 2.5 (ii) 12.4 (iii) 1.5 (iv) 4.3

(d) Determine one time when the water is 4.0 meters deep.(c) Determine the depth of the water at 9:30 am.(b) What is the minimum depth of the water? When does it occur?

PAULNELSA

LAWRENCE

On a typical day at an ocean port, the water has a maximum depth of 20 m at 8:00 am. The minimum depth of 8 m occurs 6.2 hours later. Assume that the relation between the depth of the water and time is a sinusoidal function.

(a) What is the period of the function?

(d) Determine one time when the water is 10 m deep.(c) Determine the depth of the water at 10:00 am.(b) Write an equation for the depth of the water at any time, t hours.

JUSTICEJOSEPH

THI

FRANCIS

Tidal forces are greatest when Earth, the sun, and the moon are in line. When this occurs at the Annapolis Tidal Generating Station, the water has a maximum depth of 9.6 m at 4:30 am and a minimum depth of 0.4 m 6.2 hours later.

(a) Write an equation for the depth of the water at any time, t hours.

(b) Determine the depth of the water at 2:46 pm.

BEN

RICHARDROXANNE

JOYCE

(b) How long is the water 2 meters deep or more during each period.