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.
