Asterix and Obelix are standing on skateboards on level ground 2 m apart. Obelix

Question

Asterix and Obelix are standing on skateboards on level ground 2 m apart. Obelix holds a ball of mass 1 kg. The mass of Asterix and his skateboard is 29 kg; that of Obelix and his board is 70 kg. Initially, everything is at rest; then Obelix throws the ball horizontally with an initial speed of 7 m/s toward Asterix, who will catch it and throw it back. We will ignore friction in the wheels and air resistance.

(a) Which quantity is conserved throughout the problem and why?

(b) In which direction will Obelix move after throwing the ball?
[1] to the right [2] to the left [3] not at all

(c) In which direction will Asterix move after catching the ball?
[1] to the right [2] to the left [3] not at all

(d) In which direction will the center of mass move?
[1] to the right [2] to the left [3] not at all

(e) Determine the velocity of Obelix after he has launched the ball and the velocity of Asterix after he catches the ball. Note: 7/30 = 0.23 Please draw appropriate sketches.

Explanation / Answer

(a) total momentum of asterix, obelix and the ball (b) Let us think obelix is standing to the right and asterix to the left Then, obelix moves to his right (c) to his left (d) doesn't move at all since there is no external force (e) m1v1 = m2v2 1*7 = 70*v v = 0.1 m/s After catching, both move with the same velocity. m1v1 = (m1+m2)*v2 v2 = 1*7/(29+1) = 0.23 m/s

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