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.
You have made a good attempt at modeling the event using the equation A*sin(b*t) + k, where A represents the amplitude, b represents the frequency, t represents time, and k represents the vertical shift.
To find the value for k (the vertical shift), you correctly calculated (Max + Min) / 2. In this case, the maximum height is given as 38.9 meters and the seabed level is 9.144 meters below sea level, so you converted it to positive (-9.144) and then calculated ((38.9 + (-9.144)) / 2), which gives you 14.878 meters for k.
To find the amplitude (A), you subtracted the value of k from the maximum height. In this case, you correctly calculated (38.9 - 14.878), which gives you 24.022 meters for A.
For the frequency (b), you correctly calculated the number of waves per unit of time. Since the cycle of rise and fall was given as 26-35 minutes, you calculated (2*pi / 35), which gives you approximately 0.17952 for b.
For the horizontal shift (t), you calculated half of the time period in seconds. Since the time period is given as 26 minutes, you divided it by 2*pi to convert it into seconds and obtained approximately 40.84 for t.
Putting all the values together, you correctly formed the equation:
Y = 24.022*sin(0.17952*t - 40.84) + 14.878
Now, to answer the next part of your question, you want to find out how long the water receded before the waves came crashing in at 35 minutes and at 26 minutes. To do this, you need to plug in these values into the equation and solve for Y.
1. For 35 minutes:
Y = 24.022*sin(0.17952*35 - 40.84) + 14.878
Y = 24.022*sin(6.2822 - 40.84) + 14.878
Y = 24.022*sin(-34.5578) + 14.878
Similarly, you can follow the same process to find Y for 26 minutes. However, please note that there might be limitations to this model. These limitations could include factors such as variations in the tides, other environmental factors, and the complexity of wave behavior, which may not be fully captured by a simple sinusoidal model.