Understand the Advantages of Parametric Representations
-A baseball pitcher throws a baseball with an initial velocity of 126 feet per second at an angle of $20 ^ { \circ }$ to the horizontal. The ball leaves the pitcher's hand at a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball?
A)
$\begin{array}{l}
x=118.4 \mathrm{t} ; \mathrm{y}=-16 \mathrm{t}^{2}+43.09 \mathrm{t}+5 \
2.805 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
34.012 \text { feet }
\end{array}$
B)
$\begin{array}{l}
x=118.4 t ; y=-16 t^{2}+43.09 t+5 \
5.609 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
29.012 \text { feet }
\end{array}$
C)
$\begin{array}{l}
x=118.4 \mathrm{t} ; \mathrm{y}=-16 \mathrm{t}^{2}+43.09 \mathrm{t}+5 \
2.572 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
4.985 \text { feet }
\end{array}$
D)
$\begin{array}{l}
x=118.4 t ; y=-16 t^{2}+43.09 t+5 \
5.143 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
237.094 \text { feet }
\end{array}$

Question

Quizplus · Accepted Answer

The parametric equations for the motion of the ball can be derived using the initial velocity and angle of projection. The horizontal component of the velocity is $v \cos(\theta)$ and the vertical component is $v \sin(\theta)$, where $v = 126$ ft/s and $\theta = 20^\circ$. The equations for $x(t)$ and $y(t)$ include the effects of gravity on the vertical motion, represented by $-16t^2$ (using $g = 32$ ft/s$^2$ and halving it for the equation of motion). The time of flight, time to reach maximum height, and maximum height are calculated based on these equations, making choice A the correct set of parametric equations and corresponding answers to the questions asked.

Understand the Advantages of Parametric Representations -A Baseball Pitcher Throws 20∘20 ^ { \circ }20∘

Understand the Advantages of Parametric Representations
-A Baseball Pitcher Throws $20 ^ { \circ }$