# (a) An athlete throws a basketball toward the east, with initial speed 10.6 m/s at an angle of 55.0

(a) An athlete throws a basketball toward the east, with initial speed 10.6 m/s at an angle of 55.0 above the horizontal. Just as the basketball reaches the highest point of its trajectory, it hits an eagle (the mascot of the opposing team) flying horizontally west. The ball bounces back horizontally west with 1.50 times the speed it had just before their collision. How far behind the player who threw it does the ball land? (b) This situation is not covered in the rule book, so the officials turn the clock back to repeat this part of the game. The player throws the ball in the same way. The

(a) An athlete throws a basketball toward the east, with initial speed 10.6 m/s at an angle of 55.0 above the horizontal. Just as the basketball reaches the highest point of its trajectory, it hits an eagle (the mascot of the opposing team) flying horizontally west. The ball bounces back horizontally west with 1.50 times the speed it had just before their collision. How far behind the player who threw it does the ball land? (b) This situation is not covered in the rule book, so the officials turn the clock back to repeat this part of the game. The player throws the ball in the same way. The eagle is thoroughly annoyed and this time intercepts the ball so that, at the same point in its trajectory, the ball again bounces from the birds beak with 1.50 times its impact speed, moving west at some nonzero angle with the horizontal. Now the ball hits the players head, at the same location where her hands had released it. Is the angle necessarily positive (that is, above the horizontal), necessarily negative (below the horizontal), or could it be either? Give a convincing argument, either mathematical or conceptual, for your answer.

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