(a) A balloon moves in the xy-plane according to the law x = at and y = bt, where a > 0, b> 0. Determine i the balloon's trajectory y(x) and sketch its graph. in the speed of the balloon as a function of time, t iii. the angle, ø between the velocity vector and the x-axis.

(b) Find the velocity, acceleration, and speed of a particle by the position function r(t) = 2 costi + 3 sin tj at t = 0. Sketch the path of the particle and draw the velocity and acceleration vectors for the specified values oft.