Aswimming 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?

a)

0.245 m/s

b)

0.904 m

Explanation:

a)

= speed of duck ahead of wave

= 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

= -

= 0.32 -

= 0.245 m/s

b)

= speed of wave behind the duck

speed of wave behind the duck is given as

= +

= 0.32 + 0.245

= 0.565 m/s

D = spacing between the crests

spacing between the crests is given as

D = T

D = (0.565) (1.6)

D = 0.904 m

a and b sometimes have a positive value