Posted by **Becky** on Monday, January 28, 2013 at 6:59pm.

For a boat to float in a tidal bay, the water must be at least 2.5 meters deep. The depth of the water around the boat, d(t), in meters, where t is measured in hours since midnight, is d(t)=5+4.6sin(0.5t)

Use three decimal places in all intermediate calculations.

(a) What is the period of the tides in hours?

Round your answer to three decimal places.

(b) If the boat leaves the bay at midday, what is the latest time it can return before the water becomes too shallow?

Round your answer to three decimal places.

- Pre-Calculus -
**Reiny**, Monday, January 28, 2013 at 7:49pm
a) period = 2pi/.5 = 12.663 hrs

so we need the height to be 2.5

5 + 4.6sin(.5t)= 2.5

sin(.5t) = (2.5-5)/4.6 = -.543478

make sure your calculator is set to radians and take

inverse sine(+ .543478)

to get .574575 radians

But, the sine was negative so the "angle" must have been in quadr III or quadrant IV

so .5t = pi + .574575 or .5t = 2pi - .574575

t = 7.432336 or t = 11.41722

or t = 7:26 am or t = 11:25 am

remember that midnight was t=0

so the water was below 2.5 m between

7:25 am and 11:25 am

and the period was 12.663 hrs or 12:40 hrs

so the next time the water will go below 2.5 m

= 7:25 + 12:40 = 17:65 = 18:05 or 6:05 pm

## Answer this Question

## Related Questions

- physics - A boat crosses a river, which is 60 meters wide in 15 seconds. Upon ...
- physics - The velocity of a boat with respect to the shore is 2 meters/second. ...
- physics - The velocity of a boat with respect to the shore is 2 meters/second. ...
- Math (Calculus) - A tank has the shape of an inverted circular cone with a base ...
- Math (Calculus) - A tank has the shape of an inverted circular cone with a base ...
- Calculus (Help please) - A tank has the shape of an inverted circular cone with...
- physics - A 1000 kg boat is traveling at 90 km/h when its engine is shut off. ...
- DIFF CALCULUS - A swimming pool is 12 meters long, 6 meters wide, 1 meter deep ...
- Physics - A boat weighing 9.0 × 10 2 newtons requires a horizontal force of 6.0...
- CALCULUS - Hi guys can you help me! Please teach me step by step.. I really need...