A ball is thrown with an initial speed vi at an angle θi with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/4. In terms of R and g, find the following.
(a) the time interval during which the ball is in motion
t=
(b) the ball's speed at the peak of its path
v=
(c) the initial vertical component of its velocity
yi=
(d) its initial speed
vi=
(e) the angle θi
θi=
(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.
hmax=
(g) Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range.
xmax=