An ice-skater is moving at a constant velocity across an icy pond, The skater throws a snowball directly ahead.
Which of the following correctly describes the velocity of the center of mass of the skater-snowball system immediately after the snowball is thrown?
Assume friction and air resistance are negligible.
(A) It is equal to the velocity of the snowball.
(B) It is equal to the new velocity of the skater.
(C) It is equal to half the original velocity of the skater.
(D) It is equal to the original velocity of the skater.

Respuesta :

Answer:

(D) It is equal to the original velocity of the skater.

Explanation:

The velocity of the center of mass of a system is

[tex]\vec{v}_{cm} = \frac{m1\vec{v}_1 + m_2\vec{v}_2}{m_1 + m_2}[/tex]

The velocity of the center of mass is constant if there is no external force, because the total momentum of the whole system is conserved.

So, before the snowball is thrown, the velocity of the center of mass is equal to that of the skater. This velocity will always be equal to the velocity of the center of mass of the system.

Immediately after the snowball is thrown, the velocity of the center of mass is equal to that of the skater. Option D is correct.

Velocity of the center of mass:

It is defined as the ratio of the sum of the momentum of the masses and total mass.

The velocity of the center of mass of a system given as

[tex]\bold {V_c_m = \dfrac {p_1 + p_2 } {m_1+m_2}}[/tex]

Where,

p1 - momentum of the first mass

p2 - momentum of the second mass

m1 + m1 - total mass of the system

 

If there is no external force, the velocity of the center of mass is constant because the total momentum of the whole system is conserved.

Therefore, immediately after the snowball is thrown, the velocity of the center of mass is equal to that of the skater.

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