10.7E: Parametric Equations- Graphs (Exercises)
For the following exercises, make a table of values for each set of parametric equations, graph the equations, and include an orientation; then write the Cartesian equation.
48. \(\left\{\begin{array}{l}x(t)=3 t^{2} \\ y(t)=2 t-1\end{array}\right.\)
49. \(\left\{\begin{array}{l}x(t)=e^{t} \\ y(t)=-2 e^{5 t}\end{array}\right.\)
50. \(\left\{\begin{array}{l}x(t)=3 \cos t \\ y(t)=2 \sin t\end{array}\right.\)
51. A ball is launched with an initial velocity of 80 feet per second at an angle of \(40^{\circ}\) to the horizontal. The ball is released at a height of 4 feet above the ground.
- Find the parametric equations to model the path of the ball.
- Where is the ball after 3 seconds?
- How long is the ball in the air?