Question

12. Let yo = O. Write parametric equations to represent the path of the ballsthrown by Sami and T'Aisha given the following conditions.Sami: V, = 15 ft/s, 0 = 35°, yo = 5.4 ftT'Aisha: Vo = 19 ft/s, 0 = 50°, yo = 5.8 ft13./ Make sense of problems. The senior class section is located ahorizontal distance of 40 feet from the cheerleaders and 15 feet in theair. Will either girl get her ball into the senior section? Explain youranswer.14) Let x(t) = 3t - 6 and y(t) = i- 2t model the path of one particle, andx (+) = Vt + 6 and y(t) = -3 + 2t model the path of a second particlefort > O. Model the paths of two particles in the coordinate plane. Dothese two particles ever collide? Explain.Use appropriate tools strategically. For Items 15 and 16, graph theparametric equations on the interval -4 ≤ + ≤ 4. Use a "square window."Identify each as a conic section.15. x(t) = 3P - 1, y(t) = 2t16. x(t) = 3 cos t + 1, y(t) = - 2 sin t

Answer 1

SOLUTION:

We want to write the x and y parametric equation for Sami and T'Aisha given their following data.

$\begin{gathered} Sami:v_0=15\frac{ft}{s},\theta=35^o,y_0=5.4ft \\ T^{\prime}Aisha:v_0=19\frac{ft}{s},\theta=50^o,y_o=5.8ft \\ x_0=0 \end{gathered}$

The parametric equations for x and y are given by;

$\begin{gathered} x(t)=x_0+(v_0cos\theta)t \\ y(t)=y_0+(v_0sin\theta)t+0.5gt^2 \end{gathered}$

Inserting, the values, we have; For Sami;

$\begin{gathered} Sami: \\ x\left(t\right)=15cos35t, \\ y\left(t\right)=5.4+15sin35t-16t^2 \end{gathered}$

For T'Aisha;

$\begin{gathered} T^{\prime}Aisha: \\ x\left(t\right)=19cos50t, \\ y\left(t\right)=5.8+19sin50t-16t^2 \end{gathered}$