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.