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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about 2.0 m and at high tide it is about 12.0 m. The natural period of oscillation is a little more than 12 hours and on June 30, 2009, high tide occurred at 6:45 AM. This helps explain the following model for the water depth D (in meters) as a function of the time t (in hours after midnight) on that day:

D(t) = 7 + 5 cos[0.503(t - 6.75)]

How fast was the tide rising (or falling) at the following times?

(a) 3:00 AM

(b) 6:00 AM

(c) 9:00AM

(d) Noon

(a)

To determine

To find: The velocity of the rise or fall of the tide for the timing 3:00am.

Explanation

Given:

The equation of time is given as below.

D(t)=7+5cos[0.503(t6.75)] (1)

Calculation:

Calculate the velocity of rise or fall of the tide at 3 AM.

Differentiate equation (1) with respect to t.

D'(t)=5×(sin)[0.503(t6.75)](0.503)

D'(t)=2.52sin(0.503t3.4) (2)

Substitute 3 for t in equation (2)

(b)

To determine

To find: The velocity of the rise or fall of the tide for the timing 6:00am.

(c)

To determine

To find: The velocity of the rise or fall of the tide for the timing 9:00am.

(d)

To determine

To find: The velocity of the rise or fall of the tide for the Noon.

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