Answer
$v=17.3m/s$
Work Step by Step
When the rider is sitting stationary on the seat, there is no net force exerted upon the driver, and therefore, the normal force and the rider's weight balance each other. In other words, $W=F_N=770N$
At the top of the loop, normal force and the weight support each other to give centripetal force. The sensor records $F_N=350N$ here. $$F_c=W+F_N=770+350=1120N$$ $$\frac{mv^2}{r}=1120$$ $$v=\sqrt{\frac{1120r}{m}}$$
We know $r=21m$. The rider's mass can be found by $m=W/9.8=78.57kg$
$$v=17.3m/s$$
