Momentum of System Homework: Total Momentum at h/2

[Husker70]

Homework Statement

A system initially consists of a ball of mass m at rest at a height h above the Earth and the Earth, of mass Me. When the ball has fallen a distance h/2, the total momentum of
the system is
A. 0
B. m(sqrrt)2gh
C. Me(sqrrt)2gh
D. Me + m(sqrrt)2gh
E. Me - m(sqrrt)2gh

Homework Equations

The Attempt at a Solution

I put B and missed it. I think the answer is C but not sure.
Any help understanding this would be appreciated.
Thanks,
Kevin

 

[asleight]

Homework Statement

A system initially consists of a ball of mass m at rest at a height h above the Earth and the Earth, of mass Me. When the ball has fallen a distance h/2, the total momentum of
the system is
A. 0
B. m(sqrrt)2gh
C. Me(sqrrt)2gh
D. Me + m(sqrrt)2gh
E. Me - m(sqrrt)2gh

Homework Equations

The Attempt at a Solution

I put B and missed it. I think the answer is C but not sure.
Any help understanding this would be appreciated.
Thanks,
Kevin

$$\textbf{v}_f^2=\textbf{v}_i^2+2\textbf{ad}$$

so, $$\textbf{v}=\sqrt{2\textbf{ad}}$$, and:

$$\textbf{p}=m\textbf{v}=m\sqrt{2\textbf{ad}}$$.

The total momentum of the system is the sum of momenta of the particles. The above momentum is that of the ball. The momentum of the Earth is given by:

$$M_e\textbf{v_e}=$$,

add them and that's your answer which isn't readily available, sadly. Maybe someone else has more of an intuitive approach.

 

[thomate1]

I would like to clarify the concept of momentum and how it relates to this problem. Momentum is defined as the product of an object's mass and velocity, and it is a measure of the object's motion. In this case, the system consists of two objects - the ball and the Earth. Since the ball is initially at rest, its momentum is zero. However, the Earth is constantly moving due to its rotation and revolution around the sun, so it has a non-zero momentum.

When the ball falls a distance h/2, its velocity increases and it gains momentum. At the same time, the Earth's momentum also changes due to the change in its distance from the ball. The total momentum of the system is the sum of the individual momenta of the ball and the Earth.

Since the ball's momentum is m(sqrt(2gh)) and the Earth's momentum is Me(sqrt(2gh)), the total momentum of the system at h/2 is (m+Me)sqrt(2gh). Therefore, the correct answer is option D - Me + m(sqrt(2gh)).

I would also like to mention that the equation for momentum (p = mv) is not included in the given homework statement. However, it is important to understand and use this equation to solve problems involving momentum. I hope this clarifies your understanding of the concept and helps you in solving similar problems in the future.