1. A*R*C*S Throwing a Ball.
While lying on the ground, you throw a ball that flies through the air and lands on the ground a known distance \(d\) away from you after a total time \(T\text{.}\) Find the initial velocity with which you threw the ball.
Tip.
Answer.
Part 1a from the A*R*C*S Steps can be especially helpful in keeping track of all the known and unknown quantities.
Starting with the \(x\)-direction position equation:
\begin{equation*}
v_{ix} = \frac{d}{T}
\end{equation*}
Then using the \(y\)-direction position equation:
\begin{equation*}
v_{iy} = \frac{1}{2}gT^2
\end{equation*}
And putting it all together:
\begin{equation*}
\vec{v}_{i} = \frac{d}{T}\hat{x} + \frac{1}{2}gT^2\hat{y}
\end{equation*}
