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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?

Respuesta :

Answer:

a)

0.245 m/s

b)

0.904 m

Explanation:

a)

[tex]v_{d}[/tex] = speed of duck ahead of wave

[tex]v_{s}[/tex] = 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

[tex]v_{d}[/tex] = [tex]v_{s}[/tex] - [tex]\frac{d}{T}[/tex]

[tex]v_{d}[/tex] = 0.32 - [tex]\frac{0.12}{1.6}[/tex]

[tex]v_{d}[/tex] = 0.245 m/s

b)

[tex]v_{w}[/tex] = speed of wave behind the duck

speed of wave behind the duck is given as

[tex]v_{w}[/tex] = [tex]v_{s}[/tex] + [tex]v_{d}[/tex]

[tex]v_{w}[/tex] = 0.32 + 0.245

[tex]v_{w}[/tex] = 0.565 m/s

D = spacing between the crests

spacing between the crests is given as

D = [tex]v_{w}[/tex] T

D = (0.565) (1.6)

D = 0.904 m

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