(a) A boy sitting in a railroad car moving at constant velocity throws a ball straight up into the air, according to the person sitting next to him. Where will the ball fall?

(A) Behind him (B) In front of him

(e) Into his hands (D) Beside him

(b) Where would the ball fall if the train accelerates forward while the ball is in the air? If it rounds a curve?

(A) Behind him (B) In front of him

(C) Into his hands (D) Beside him

The correct option is:
(a) (C) into his hands.
(b) (A) behind him.

(a)Neglecting the effect of air on the ball thrown upward by the boy siting on a railroad car moving with constant velocity, the person sitting next to him will observe the ball moving back in the boy’s hand. This is so because the boy, the person and the ball are all in the same frame of reference and are moving with the same velocity.This is similar to the effect when the person observer the phenomenon when all were on ground while the Earth itself rotates.
Therefore, (C) is the correct option and the rest are ruled out.

(b) If the train accelerates forward, the person and the boy will move forward relative to the ball when it moves upward with time. The relative forward displacement of the boy and person relative to ball does not allow the boy and person to be at the same place as the ball when it reaches down. As a result, the ball will appear to have fallen behind the boy.Therefore (A) is the correct option and the rest are ruled out.