Answer
$y_m = 0.16~m$
Work Step by Step
If the rope is oscillating in fundamental mode, then the midpoint $x = 1.0~m$ is an antinode. If the transverse displacement is zero, then the point $x = 1.0~m$ is moving at maximum speed.
We can find the amplitude:
$v_{max} = y_m~\omega = 5.0~m/s$
$y_m~2\pi f = 5.0~m/s$
$y_m = \frac{5.0~m/s}{2\pi f}$
$y_m = \frac{5.0~m/s}{(2\pi)(5.0~Hz)}$
$y_m = 0.16~m$
