Answer
(a) The boat encounters a wave crest every 1.4 seconds.
(b) The boat encounters a wave crest every 11 seconds.
Work Step by Step
(a) If the boat is moving west, the speed of the wave is 32 m/s relative to the boat. We can find the time it takes for the wave to travel a distance of 44 meters at this relative speed.
$t = \frac{44~m}{32~m/s} = 1.4~s$
The boat encounters a wave crest every 1.4 seconds.
(b) If the boat is moving east, the speed of the wave is 4 m/s relative to the boat. We can find the time it takes for the wave to travel a distance of 44 meters at this relative speed.
$t = \frac{44~m}{4~m/s} = 11~s$
The boat encounters a wave crest every 11 seconds.