Consider the following parametric equations. x=t2t+6, y=t3 - 3t Use a graphing utility to graph the curve represented by the parametric equations. (a) Use a graphing utility to find dx dy dt dt dy and at the parameter t = -1. dx dx = dt dy dt dy dx (b) Find an equation of the tangent line to the curve at the parameter t = -1. Use a graphing utility to graph the curve and the tangent line.

Sketch and describe the orientation of the curve given by the parametric equations x=2tandy=4t2+2,2t2.

Shooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the path of a projectile with initial speed v0=32ft/s, fired into a headwind of =24ft/s, for the angles =5,15,30,40,45,55,60 and 75. Is it still true that the greatest range is attained when firing at 45 ? Draw some more graphs for different angles, and use these graphs to estimate the optimal firing angle.