(Solved): please answer part b and c Problem 1: Using air pressure, the \( 0.25 \mathrm{~kg} \) ball is forced ...

Problem 1: Using air pressure, the \( 0.25 \mathrm{~kg} \) ball is forced to move through the tube lying in the horizontal plane and having the shape of a logarithmic spiral. Assume that the tangential force exerted on the ball due to the air is \( F=4 \mathrm{~N} \). Determine: (a) the rate of increase in the ball's speed at the instant \( \theta=\frac{\pi}{3} \), (b) the acceleration of the ball in the radial direction at the same instant, and (c) the direction of the the tangential force exerted on the ball at the same instant (this is the angle that the tangential force \( F \) makes with positive direction of the \( x \)-axis counted counterclockwise). Note: To get full credit, please, respond correctly and show all the details of the solution process, including free-body diagram, labels, and reference systems.