Pre-Cal 40S Slides March 12, 2008
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Transcript of 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.
(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.