104 Motion in Two DimensionsP4.55The special conditions allowing use of the horizontal range equation applies.For the ball thrown at 45°,DRvgi==45290sin.For the bouncing ball,DR Rvggivi=+=+1222222sinsinθejwhere is the angle it makes with the ground when thrown and when bouncing.(a)We require:vgvgvgiii222424526 6=+==°sinsinsin.θθFIG. P4.55(b)The time for any symmetric parabolic flight is given byyvtgtvtgtfyi=−1201222sin.If t=0 is the time the ball is thrown, then
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Ratio, Sin, Manifold, Spacetime, Two Dimensions, vi2 sin