Calculate the final velocity of an object accelerating towards a mass

[wildkat7411]

I need to be able to calculate the final velocity of an object accelerating towards a mass from a distnce with an initial velocity. From my little knowledge of calculus, I am only a junior in high school, i have figured out that this is probably a derivative problem. But i have no knowledge of how to solve these kinds of equations. If I am right would some one please walk me through it step-by-step. If I'm wrong, please correct me and show me how to do it step by step. This is not a homework problem but a problem i made up to challenge myself. The problem is i think I am in way over my head. So any help would be amazing. Thanks

 

[bapowell]

No, I think all you need here is to apply conservation of energy,

$$\Delta KE = -\Delta PE$$,

where PE is the gravitational potential energy between the two objects.

 

[wildkat7411]

But since acceleration due to gravity increases as the distance between the two objects decreases, you can't use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.

 

[bapowell]

But since acceleration due to gravity increases as the distance between the two objects decreases, you can't use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.

Right, you can't use $$PE = mgh$$. Use Newton's Law of Gravitation.

 

[Janus]

But since acceleration due to gravity increases as the distance between the two objects decreases, you can't use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.

No you can't. you have to use

$$PE = -\frac{GMm}{r}$$

Where r is the distance between the centers of m and M.

Just remember that $\Delta PE$ is the difference in PE between the start of the fall and the end of the fall.