Power is defined as the rate at which work is done. In this case, the work done by the cyclist is equal to the force she overcomes (30N) multiplied by the distance she travels (30m). Therefore, the work done is:

$$W = Fd = (30N)(30m) = 900 J$$

The power is then calculated by dividing the work done by the time taken:

$$P = \frac{W}{t} = \frac{900 J}{6 s} = 150 W$$

Therefore, the power of the cyclist is 150 W.