Problem 3 Asterix and Obelix are standing on skateboards on level ground 2 m apa

Question

Problem 3 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) Add a coordinate system to the calculate the center of mass when everything is at figure and rest. (b) Which quantity is conserved throughout the problem and why? (c) In which direction will Obelix move after throwing the ball? (1) to the right [2] to the left 13]not at all (d) In which direction will Asterix move after catching the ball? [1] to the right 2 to the left [3] not at all (e) In which direction will the center of mass move? [1] to the right [2] to the left [3]not at all (f 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

Here,

mass of obelix , m1 = 70 Kg

mass of asterix , m2 = 29 Kg

initial speed ball , u = 7 m/s

a)

let asterix is at origin , and the positive direction points to the right

centre of mass = m1 * d/(m1 + m2)

centre of mass = 70 * 1 /(70 + 29)

centre of mass = 0.71 m

b)

as there is no external force acting on system in horizontal direction.

The momentum is conserved.

c)

as he throw ball to the left

the Obelix will move to the right (option 1)

d)

as the direction of motion of ball is to the left

Asterix will move to the left (option 2)

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