Slackline is a sport in which the athlete must balance and perform maneuvers while standing on a stretched ribbon. For the practice of the sport, the two ends of the ribbon are fixed so that it is a few centimeters from the ground. When an athlete with a mass equal to 80 kg is exactly in the middle of the ribbon, it moves vertically, forming an angle of $10^{\circ}$ with the horizontal, as shown in the figure. It is known that the acceleration due to gravity is equal to $10 \mathrm{~m~s}^{-2}$, $\cos\left(10^{\circ}\right) = 0.98$ and $\sin\left(10^{\circ}\right) = 0.17$. What is the force that the ribbon exerts on each of the trees because of the presence of the athlete? (A) $4.0 \times 10^{2} \mathrm{~N}$ (B) $4.1 \times 10^{2} \mathrm{~N}$ (C) $8.0 \times 10^{2} \mathrm{~N}$ (D) $2.4 \times 10^{3} \mathrm{~N}$ (E) $4.7 \times 10^{3} \mathrm{~N}$
Slackline is a sport in which the athlete must balance and perform maneuvers while standing on a stretched ribbon. For the practice of the sport, the two ends of the ribbon are fixed so that it is a few centimeters from the ground. When an athlete with a mass equal to 80 kg is exactly in the middle of the ribbon, it moves vertically, forming an angle of $10^{\circ}$ with the horizontal, as shown in the figure. It is known that the acceleration due to gravity is equal to $10 \mathrm{~m~s}^{-2}$, $\cos\left(10^{\circ}\right) = 0.98$ and $\sin\left(10^{\circ}\right) = 0.17$.
What is the force that the ribbon exerts on each of the trees because of the presence of the athlete?\\
(A) $4.0 \times 10^{2} \mathrm{~N}$\\
(B) $4.1 \times 10^{2} \mathrm{~N}$\\
(C) $8.0 \times 10^{2} \mathrm{~N}$\\
(D) $2.4 \times 10^{3} \mathrm{~N}$\\
(E) $4.7 \times 10^{3} \mathrm{~N}$