Answer
She has to wait for 7.08 s for the next wave.
Work Step by Step
Here we use the equation $V=\sqrt {\frac{\lambda g}{2\pi}}$ to find the speed of the wave. where V - speed of the wave, $\lambda$ - wave length, g - gravitational acceleration.
$V=\sqrt {\frac{\lambda g}{2\pi}}$ ; Let's plug known values into this equation.
$V=\sqrt {\frac{78.2m\times 9.8m/s^{2}}{2\pi}}=11.04\space m/s$
Let's apply the equation $S=ut$ to find the waiting time of the surfer. where S - displacement of the wave, u - speed of the wave, t - time.
$S=ut$ ; Let's plug known values into this equation.
$78.2m=11.04\space m/s\times t$
$t=7.08\space s$
She has to wait for 7.08 s for the next wave.
