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Good for you doing math homework with your child.

As others have mentioned, the question and answer as written is flawed. The correct answer is of course E Only.

However there is one condition where B could have zero kinetic energy. That would be if the frame of reference is moving at exactly the same speed as the ball is moving when at the top of the first peak but in the opposite direction.

That is, if the entire thing above is inside a railway car moving left, and you are watching from beside the track.

However, that would make the answer B only, without the E.

If the train stopped between the time the ball passed B and reaching E, I guess B and E is possible.

Bonus Point: The soccer ball needs air if it bounced like that, or the floor is made of jello.

Good for you doing math homework with your child.

As others have mentioned, the question and answer as written is flawed. The correct answer is of course E Only.

However there is one condition where B could have zero kinetic energy. 

That would be if the frame of reference is moving at exactly the same speed as the ball is moving when at the top of the first peak.

That is, if the entire thing above is inside a railway car that accelerates right to that exact speed as the ball reaches B, and you are watching from inside the car.

If the train car then decelerated back to the initial velocity after the ball passed B and reaches E, I guess B and E is possible.

Mind you, the curve for the first loop would look significantly contracted.

Bonus Point: The soccer ball needs air if it bounced like that, or the floor is made of jello.

Good for you doing math homework with your child.

As others have mentioned, the question and answer as written is flawed. The correct answer is of course E Only.

However there is one condition where B could have zero kinetic energy. That would be if the frame of reference is moving at the same speed as the ball is moving at the top of the first peak but in the opposite direction.

That is, if the entire thing above is inside a railway car moving left, and you are watching from beside the track.

However, that would make the answer B only, without the E.

If the train stopped between the time the ball passed B and reaching E, I guess B and E is possible.

Bonus Point: The soccer ball needs air if it bounced like that, or the floor is made of jello.

Good for you doing math homework with your child.

As others have mentioned, the question and answer as written is flawed. The correct answer is of course E Only.

However there is one condition where B could have zero kinetic energy. That would be if the frame of reference is moving at exactly the same speed as the ball is moving when at the top of the first peak but in the opposite direction.

That is, if the entire thing above is inside a railway car moving left, and you are watching from beside the track.

However, that would make the answer B only, without the E.

If the train stopped between the time the ball passed B and reaching E, I guess B and E is possible.

Bonus Point: The soccer ball needs air if it bounced like that, or the floor is made of jello.

Good for you doing math homework with your child.

As others have mentioned, the question and answer as written is flawed. The correct answer is of course E Only.

However there is one condition where B could have zero kinetic energy. That would be if the frame of reference is moving at the same speed as the ball is moving at the top of the first peak but in the opposite direction.

That is, if the entire thing above is inside a railway car moving left, and you are watching from beside the track.

However, that would make the answer B only, without the E.

Bonus Point: The soccer ball needs air if it bounced like that, or the floor is made of jello.

Good for you doing math homework with your child.

As others have mentioned, the question and answer as written is flawed. The correct answer is of course E Only.

However there is one condition where B could have zero kinetic energy. That would be if the frame of reference is moving at the same speed as the ball is moving at the top of the first peak but in the opposite direction.

That is, if the entire thing above is inside a railway car moving left, and you are watching from beside the track.

However, that would make the answer B only, without the E.

If the train stopped between the time the ball passed B and reaching E, I guess B and E is possible.

Bonus Point: The soccer ball needs air if it bounced like that, or the floor is made of jello.