a .140 kg baseball is dropped from rest from a height of 2.2m above the ground. it rebounds to a height of 1.6 m. what change in the balls momentum occurs when the ball hits the ground?

To determine the change in momentum when the ball hits the ground, we need to calculate the initial and final velocities of the ball. We can use the principles of conservation of energy to do this.

First, let's calculate the initial velocity of the ball just before it hits the ground.
We can use the conservation of energy, which states that the initial potential energy of the ball is converted into its final kinetic energy.
The initial potential energy formula is PE = mgh, where m is the mass of the ball (0.140 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the initial height (2.2 m).
So, the initial potential energy of the ball is PE = 0.140 kg * 9.8 m/s² * 2.2 m = 3.429 Joules.

Next, let's calculate the final velocity of the ball just after rebounding.
Since the ball rebounds to a height of 1.6 m, we can apply the conservation of energy again to find its final velocity.
The final potential energy formula is PE = mgh, where the potential energy is converted into kinetic energy.
Here, h is the final height (1.6 m).
Setting the initial potential energy equal to the final potential energy, we have:
mgh = 0.5mv², where v is the final velocity.
Simplifying the equation, we get:
v = √(2gh)
v = √(2 * 9.8 m/s² * 1.6 m)
v ≈ 6.23 m/s

Now we have the initial velocity (before hitting the ground) and final velocity (just after rebounding).
The change in momentum can be found using the formula:
Change in momentum = Final momentum - Initial momentum

Since momentum is equal to mass multiplied by velocity (p = mv), we can calculate the change in momentum:
Change in momentum = m * v - m * (-v)

Substituting the values:
Change in momentum = 0.140 kg * 6.23 m/s - 0.140 kg * (-6.23 m/s)
Change in momentum ≈ 1.74 kg·m/s

Therefore, the change in momentum when the ball hits the ground is approximately 1.74 kg·m/s.

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