Chapter 10.1, Problem 19ES

(a) Use a graphing utility to generate the trajectory of a housefly whose equations of motion over the time interval $0\le t\le 5$ are $x=6t-\frac{1}{2}{t}^3,y=1+\frac{1}{2}{t}^2$

(b) Make a table of x- and y-coordinates of the fly at times $t=0,1,2,\text{3},4,5.$

(c) At what times is the fly on the y-axis?

(d) During what time interval is $y<5?$

(e) At what time does the x-coordinate of the housefly reach a maximum?