I'm confused about the following simple circular motion question.
A water skier of mass 100 kg is being towed by a speed boat, the length of the tow rope being 30 meters. Boat and skier are moving with constant speed in concentric circles of radii of 40 meters and 50 meters respectively. The total mass of the boat and its occupant is 300 kg and its speed is 8 m/s while the speed of the skier is 10 m/s. Assuming that the tow rope is horizontal and the total air and water resistance is proportional to the square of the speed (with the same constant of proportion for both boat and skier), find the tension in the tow row and the magnitude and direction of the force driving the speed boat.
Attached is a diagram I have constructed for the scenario. The friction of the skier is $F_s$. The friction of the speed boat is $F_b$ and the tension of the tow rope is $T$. The direction of motion is shown in the diagram.
My question is: Why is the driving force of the speed boat at an angle to the tangent?
The answer to the question is.
$ 519 N $ at $ \tan^{-1} \dfrac{46}{16}$ with tangential direction.
However I think this answer is incorrect.
