Please!! I really need to get this done but I'm not sure how! HELP!?

Question

While riding in your boat, you notice one wave pass by every two seconds. If the actual frequency of the waves is

1 Hz, with what speed are you moving through the water?

(The speed of the wave is 5 m/sec)

Answer 1

Okay, let's reason it out together.  If you were traveling at 5 ms/Sec in same direction as the waves, then you would stay at the same point relative to the whole wave herd and they would never pass you by at all.  If you were standing still, you'd see one wave per second pass you by.  If you were traveling into the waves at 5 m/S ground speed and the distance between waves is [Lambda = v/f = 5 m/S / 1 wave/S = 5 m/wave], then during the one second that you travel one entire wavelength, two of them would pass you by because your speed relative to the waves is actually 10 m/S (5 for you and 5 for them in opposite direction).  You would then see 2 waves/S since distance between waves is 5 m.  This leads us to a general equation:

W = (Vwaves + Vboat) / Lambda, or

W =  (5 + Vboat) / 5

   where W is number of waves passing boat per second and Vwaves is ground speed of waves, Vboat is boat speed in direction opposite to wave direction, and Lambda is wavelength.

Transposing to find Vboat, Vboat = 5W - 5.

Since W = 1/2 (given), Vboat = 5/2 - 5, or -5/2.  Since sign is negative, boat is traveling with waves at 5/2 m/S, which should be answer 'e'.

There, now wasn't that easy?

Answer 2

V=lambda x f

V=5 m/s x 1 Hz

V=5 m/s squared