Answer :
The combined bullet and baseball will rise 40.8 mm after the collision.
We can use the law of conservation of momentum to solve for the height to which the combination of the bullet and baseball will rise after the collision. Before the collision, the total momentum of the system is zero because the baseball is at rest. After the collision, the total momentum of the system is equal to the momentum of the combined bullet and baseball.
Let's call the final velocity of the combined bullet and baseball "vf". The momentum of the combined bullet and baseball before the collision is equal to the momentum after the collision:
0 = m_bullet * v_bullet + m_baseball * 0
where m_bullet is the mass of the bullet and v_bullet is the velocity of the bullet before the collision. After the collision, the momentum of the combined bullet and baseball is:
m_total * vf = m_bullet * v_bullet + m_baseball * vf
where m_total is the combined mass of the bullet and baseball and vf is the final velocity of the combined bullet and baseball.
Solving for vf, we get:
vf = m_bullet * v_bullet / m_total
where m_total = m_bullet + m_baseball.
Next, we can use the equation of motion to find the height to which the combination will rise:
h = vf^2 / (2 * g)
where h is the height, vf is the final velocity, and g is the acceleration due to gravity.
Putting it all together:
m_total = m_bullet + m_baseball
=> 0.027 kg + 0.15 kg
=> 0.177 kg
vf = m_bullet * v_bullet / m_total
=> 0.027 kg * 112 m/s / 0.177 kg
=> 0.804 m/s
h = vf^2 / (2 * g)
=> 0.804 m/s^2 / (2 * 9.8 m/s^2)
=> 0.0408 m
=> 40.8 mm
To learn more about Collisions :
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