Answer
The tension in the rope is 3590 N.
Work Step by Step
The vertical component of the tension in each side of the rope provides the force to accelerate the person up in the air. Let $T$ be the tension in each side of the rope. Note that $T_y = T~sin(\theta)$.
We can set up a force equation to find $T$:
$\sum F = ma$
$2T_y - mg = ma$
$2T~sin(\theta) = m(g+a)$
$T = \frac{m(g+a)}{2~sin(\theta)}$
$T = \frac{(70~kg)(9.80~m/s^2+8.0~m/s^2)}{2~sin(10^{\circ})}$
$T = 3590~N$
The tension in the rope is 3590 N