Answer:
velocity = 3.42 m/s
T = 2.19 s
wavelength = 0.4056 m
Explanation:
given data
wavelength λ = 7.50 m
to find out
velocity , period T and wavelength when time 3.92 s
solution
we will apply first velocity formula that is
velocity = [tex]\sqrt{\frac{wavelength*g}{2\pi } }[/tex] ..............1
put here all value g = 9.8, wavelength = 7.50
velocity = [tex]\sqrt{\frac{7.50*9.8}{2\pi } }[/tex]
velocity = 3.42 m/s
and
time formula that is
velocity = wavelength × f ..............2
here f is frequency = 1/T .............3
so
velocity = wavelength × 1/T ..............4
T = [tex]\frac{wavelength}{velocity}[/tex]
T = [tex]\frac{7.50}{3.42}[/tex]
T = 2.19 s
and
wavelength by time 3.92
relation between wavelength and time is express as
T = [tex]\frac{wavelength}{\sqrt{\frac{wavelength*g}{2\pi } } }[/tex] .............4
so
3.92 = [tex]\frac{wavelength}{\sqrt{\frac{wavelength*9.8}{2\pi } } }[/tex]
3.92 = [tex]\frac{wavelength}{\sqrt{wavelength*1.5597}}[/tex]
6.076 × wavelength = √wavelength
√wavelength = 1 / 6.076
wavelength = 0.4056 m
