A cue ball is shot at a 45 degree angle from the upper right corner of a billiard table with dimensions 4 ft by 5 ft, as shown. How many times does the ball bounce before hitting another corner? Assume that when the ball
bounces, its path is perfectly reflected. The final impact in the corner does not count as a bounce.
[asy]
size(120);
draw((0,0)--(5,0)--(5,4)--(0,4)--cycle);
label("5",(0,0)--(5,0),S);
label("4",(0,0)--(0,4),W);
filldraw(circle((0.4,3.6),0.4),black);
draw((0,4)--(1.5,2.5),EndArrow);
draw((1.5,2.5)--(4,0)--(5,1), dashed);
draw(arc((0,4),1.25,315,270));
label(scale(0.8)*"45∘",(0.2,2.8),SE);
[/asy]
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>4<spanclass=′latex−bold′>(C)</span>5<spanclass=′latex−bold′>(D)</span>6<spanclass=′latex−bold′>(E)</span>7