Question

A boat is moving to the right at 5.0 m/s with respect to the water. An ocean wave is moving to the left, opposite the motion of the boat. The waves have 2.0 m between the top of the crests and the bottom of the troughs. The period of the waves is 8.3 s, and their wavelength is 110 m. The water wave acts like a cosine function as ?(?, ?) = ? cos(?? + ?? + ?). At one instant, the boat sits on a crest of the wave. 20 seconds later, find the vertical displacement of the boat. Hint: To solve the problem, one should find the final position of the boat after 20 seconds.

y(x, t) A cos(kx + at + φ)

Answer 1

Consider the above given that period of wave = 8.3 s wavelength = 110 m velocity of the ocean waves V_wave = lambda/T = 110/8.3 = 13.25 m/s the boat is moving towards the right at = 5 + 13.25 = 18.25 m/ s total distance d = 18.25 times t = 18.25 times 20 = 365 m Total system T' = lambda/v_net = 110/18.25 almostequalto 6.03 sec The waves are sinusoidal y = A cos omega t y = 1 cos (59.7 times 20) = -0.406 m