A soccer ball rolls out of a gym through the center of a doorway into the next room, the adjacent room is 6.00 m by 6.00 m with the 2.00-m wide doorway located at the center of the wall. The ball hits the center of a side wall at 45.0°. If the coefficient of restitution for the soccer ball is 0.700, does the ball bounce back out of the room? (Note that the ball rolls without slipping, so no energy is lost to the floor.)

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