Posted by Amanda on .
swimming duck paddles the water with it's feet once every 1.6s, producing surface waves with this perios. The duck is moving with constant speed in a pond where the speed of the surface waves is 0.32m/s and the crests of the waves are 0.12m apart.
A) What is the duck's speed?
B)How far apart are the crests behind the duck
If you can only answer part of the question, that's okay. Thanks

Physics 
drwls,
It already says the crests of the waves are 0.12 m apart, but I suspect that may be for the forward direction. They will be farther apart behind the duck, because it moves away before the next paddle.
The duck creates a wave with each paddle. The wave moves 0.32 m/s * 1.6 s = 0.512 ahead with each paddle, but 0.12 m behind each crest there is a new wave, indicating that the duck moved 0.392 m in 1.6 s. The duck's speed is 0.392 m/1.6 s = 0.245 m/s. The duck is traveling at 76% of the wave speed, reducing the wave separation ahead of it.
Behind the duck, the distance between wave crests is the distance a wave travels in 1.6 s (0.512 m PLUS the distance that the duck has moved away in that time, 0.392 m. The total wave separation is 0.904 m.