A ball is thrown with an initial speed v; at an angle 0; with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/8. In terms of R and g, find the following. (a) the time interval during which the ball is in motion 2 t = (b) the ball's speed at the peak of its path gR cot(0. st (0 ;) 2 V = (c) the initial vertical component of its velocity gR tan () 2 Vi, Y (d) its initial speed RG V = 2.236 4 X (e) the angle 8; expressed in terms of arctan of a fraction. 0,= 26.565 0 X X = (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. max = 0.624962 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. Xmax 1.249924 X