Answer
The rider needs a power output of $147~Watts$
Work Step by Step
We can find the vertical height increase each second if the bicycle moves at a speed of 4.0 m/s:
$h = (0.05)(4.0~m) = 0.20~m$
We can find the change in gravitational potential energy each second:
$U_g = mgh = (75~kg)(9.80~m/s^2)(0.20~m) = 147~J$
Since the rider needs to do $147~J$ or work each second, the rider needs a power output of $147~Watts$
