Question

A swimming duck paddles the water with its feet once every 1.6 s, producing surface waves with this period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.32 m/s, and the crests of the waves ahead of the duck are spaced 0.12 m apart. (a) What is the duck's speed? (b) How far apart are the crests behind the duck?

Answer 1

a)

0.245 m/s

b)

0.904 m

Step-by-step explanation:

a)

`v_(d)` = speed of duck ahead of wave

`v_(s)` = speed of surface wave = 0.32 m/s

T = time for paddling = 1.6 s

d = spacing between the waves = 0.12 m

speed of duck ahead of wave is given as

`v_(d)` =
`v_(s)` -
`(d)/(T)`

`v_(d)` = 0.32 -
`(0.12)/(1.6)`

`v_(d)` = 0.245 m/s

b)

`v_(w)` = speed of wave behind the duck

speed of wave behind the duck is given as

`v_(w)` =
`v_(s)` +
`v_(d)`

`v_(w)` = 0.32 + 0.245

`v_(w)` = 0.565 m/s

D = spacing between the crests

spacing between the crests is given as

D =
`v_(w)` T

D = (0.565) (1.6)

D = 0.904 m