Question

A boat is traveling at 3.2 m/s in the same direction as an ocean wave of wavelength 30 m and speed 6.8 m/s. If the boat is on the crest of a wave, how much time will elapse until the boat is next on a crest?

Answer 1

To solve this problem we apply the kinematic equations of linear motion. For which the speed is described as the distance traveled in a time interval. This would be,

$v = \frac{x}{t} \rightarrow t = \frac{x}{v}$

Our values are given as,

$\text{The speed of the boat} = v_b = 3.8m/s$

$\text{The speed of the ocean} = V = 6.8m/s$

$\text{The wave length of the wave is the same distance traveled by boat} = d = \lambda = 30m$

$\text{The relative speed of the boat} = v_r = -3.8 +6.8 = 3m/s$

Replacing we have,

$t = \frac{d}{v_r}$

$t = \frac{30m}{3m/s}$

$t = 10s$

Therefore will take until the boat is next on a crest around to 10s