Zoroaster Planet Escape Speed Calculation for Meteor Collision

[~*Noor*~]

Q.) The escape speed from the surface of Planet Zoroaster is 15.0 km/s. The planet has no atmosphere. A meteor far away from the planet moves at speed 5.0 km/s on a collision course with Zoroaster. How fast is the meteor going when it hits the surface of the planet?

My answer:

15+5=20km/s since they both are going towards each other. But keep getting this answer wrong...i've tried 15km/s as well which is also wrong

What am i doing wrong here?

 

[Gear300]

The escape speed is not the translational speed of the planet. Its the the speed required to leave the planet. You'll have to take into account the acceleration of the meteor given by the planet's gravitational field. Since the meteor is far away from the planet at first, you can assume the initial acceleration to be around 0 m/s^2. But as the meteor approaches the planet, it will accelerate towards it.

 

[baba89]

There are a few things to consider when solving this problem. First, it is important to understand that the escape speed is the minimum speed needed for an object to escape the gravitational pull of a planet and not be pulled back. In this case, the escape speed of Planet Zoroaster is 15.0 km/s, meaning that any object traveling at this speed or higher will be able to escape the planet's gravitational pull.

Next, we need to take into account the initial speed of the meteor, which is 5.0 km/s. Since the meteor is already moving towards the planet at this speed, we need to add this to the escape speed to determine the total speed at which the meteor will hit the surface of the planet.

Therefore, the correct answer is 20.0 km/s. This is because the meteor is already moving towards the planet at 5.0 km/s and it needs to reach the escape speed of 15.0 km/s to escape the planet's gravitational pull, resulting in a total speed of 20.0 km/s when it hits the surface.

It is important to note that this calculation assumes that there are no other forces acting on the meteor, such as air resistance or gravity from other celestial bodies. In reality, these factors may affect the speed of the meteor as it approaches the planet. Additionally, the exact speed at which the meteor hits the surface may vary depending on the angle and trajectory of its collision.