$($a$)$ the time interval during which the ball is in motion

$($b$)$ the ball's speed at the peak of its path

$v=\sqrt[\phantom{2}]{\frac{gRcot({}_i)}{2}}$

$($c$)$ the initial vertical component of its velocity

$v_{i,y}=\sqrt[\phantom{2}]{\frac{gRtan({}_i)}{2}}$

$($d$)$ its initial speed

$v_i=2\mathrm{.}236\sqrt[\phantom{2}]{\frac{RG}{4}}$

$($e$)$ the angle ${}_i$ expressed in terms of arctan of a fraction.

${}_i=$

$($f$)$ Suppose the ball is thrown at the same initial speed found in $($d$)$ but at the angle appropriate for reaching the greatest height that it can. Find this height.

$h_{\text{m}\text{a}\text{x}}=$

$($g$)$ Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range.

$x_{\text{m}\text{a}\text{x}}=$