Answer
$t=11.9s$
Work Step by Step
We can determine the required time as follows:
$tan\theta=\frac{8}{2\pi r}=\frac{8}{2\pi(8)}$
$\implies \theta=9.04^{\circ}$
We know that:
$\Sigma F_y=0$
$\implies N-Wcos\theta=0$
$\implies N-800cos 9.04=0$
$\implies N=790.1lb$
The final tangential speed of the car is given as
$mr_1v_1+\int_0^t hNsin\theta dt=mrv_t$
We plug in the known values to obtain:
$0+\int_0^t 8\times 790.1 sin 9.04 dt=\frac{800}{32.2}\times 8\times 60cos 9.04$
This simplifies to:
$t=11.9s$
