# Calculate the final velocity of an object accelerating towards a mass

1. Feb 26, 2010

### 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, im only a junior in high school, i have figured out that this is probably a derivitive problem. But i have no knowledge of how to solve these kinds of equations. If im 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 im in way over my head. So any help would be amazing. Thanks

2. Feb 26, 2010

### bapowell

Re: Gravity

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.

3. Mar 1, 2010

### wildkat7411

Re: Gravity

But since acceleration due to gravity increases as the distance between the two objects decreases, you cant 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.

4. Mar 1, 2010

### bapowell

Re: Gravity

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

5. Mar 1, 2010

### Janus

Staff Emeritus
Re: Gravity

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.