Question

Before a tidal wave the sea level usually drops first leaving the seabed exposed. (normally about 30 feet below sea level) then it rises an equal distance above sea level. Waves hitting a city with a maximum height of 38.9 meters. The cycle of rise and fall was 26-35 minutes with the waves following the sine curve (height Y of the tsunami wave varies sinusoidally with time t) make a model to describe the event.
1. Use A*sin(b*t) + k
2. How long did the water recede before the waves came crashing in at 35 minutes and at 26 minutes. Does this model have limitations
-H-shift I did (Max+min/2) with 30 feet converted to 9.144 meters. (38.9+(-9.144)/2)=14.878 meters=K
-for Amplitude I got 38.9-14.878= 24.022 =A
Frequency was 1wave every 35 minutes so I did( 2pi/35)=.17952=b and V-shift(26/2pi)=40.84= t
So for the equation I got 24.022 sin (.17952x-40.84) + 14.878
Someone please help me, I've been struggling with this to the max, I'll be grateful for any type of help at all.

Answer 1

Hmmm. It says "the waves came crashing in at 35 minutes and at 26 minutes". That sounds like a period of 9 minutes, so I'd make b=2pi/9 rather than 2pi/35.

so, for #2, I'd say the water receded for 4.5 minutes before crashing in.

Other than that, your work looks good.

Answer 2

ohh no i meant to write if it came at 35 and what if it came at 26, but that's great, thanks alot for looking over it!!!!