Question

A penguin has decided to jump between two small icebergs floating in the ocean near Antarctica. You may neglect water resistance and treat the motion of the icebergs relative to the water as frictionless. At the beginning of the problem all are at rest with respect to each other. The penguin runs and jumps off the first iceberg and land on the second, where it comes to rest relative to the second iceberg. The mass of the penguin is mp. The two icebergs each have a mass of mice. The penguin jumps with a speed of vp at an angle γp.Find the final relative speed of the two icebergs.

Answer 1

Initially iceberg 1 and penguin are at rest. when penguin jumps off the first iceberg with velocity making an angle , iceberg 1 moves  with velocity .

As the iceberg moves away in the horizontal direction, the horizontal velocity of penguin only must be used in conserving momentum in horizontal direction.

Velocity of iceberg 1 is

Velocity of penguin w.r.t iceberg 1 is

Conserving momentum of iceberg+ penguin, before and after the penguin jumps off,

Velocity of iceberg 1 is

Negative sign indicates that first iceberg is moving away in a direction opposite to that of penguin.

Now penguin with its horizontal velocity jumps onto 2nd iceberg which is at rest., again conserving the horizontal momentum of penguin and iceberg 2,

Velocity of iceberg 2 is

Final relative speed of two icebergs is