Pregunta
An incoming meteor with mass 65.4 kg
and velocity
another meteor with mass 32.1 kg and
velocity
stick together. What is their velocity?
and velocity
another meteor with mass 32.1 kg and
velocity
stick together. What is their velocity?
Ask by Lyons Higgins. in South Africa
Jan 22,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The velocity of the combined meteors after they stick together is approximately 11.176 km/s.
Solución
To find the velocity of the two meteors after they stick together, we need to consider the conservation of momentum. The momentum of an object is given by the product of its mass and velocity.
Given:
- Mass of the first meteor:
- Velocity of the first meteor:
- Mass of the second meteor:
- Velocity of the second meteor:
Let’s denote the velocity of the combined meteors as
The momentum of the first meteor before the collision is
After the collision, the combined mass of the meteors is
The conservation of momentum can be expressed as:
Now, we can solve for the velocity
Solve the equation by following steps:
Solve the equation by following steps:
- step0: Solve for
:
- step1: Simplify:
- step2: Swap the sides:
- step3: Divide both sides:
- step4: Divide the numbers:
The velocity of the combined meteors after they stick together iskm/s, which is approximately 11.176 km/s.
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Simplifique esta solución Beyond the Answer
To find the final velocity of the two meteors after they collide and stick together, we can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.
The momentum for each meteor is given by the formula:
Calculating the momentum of each meteor:
- For the first meteor:
- For the second meteor:
Total momentum before the collision:
Since the two meteors stick together after the collision, the combined mass
Using the conservation of momentum to find the final velocity
Therefore, the final velocity of the two meteors stuck together is approximately
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